good news and bad news
Bottom line it is worth putting in the carb heat door in and think it would be negligent and dangerous not to install it. I also suggest using a much more substantial control cable to activate the door. The wire type fails with in 100-300 hours, and will continue to do so. The cable I refer to has a solid rod end like the mixture or throttle with a threaded tip, but it has a simple small knob. They cost more and weigh more but worth it.
The good news is Lycoming carbs are less subject (but not immune) to carb ice like other engines, such as continental. Also the good part is the flapper door does work. It does provide warmer temps and an alternate path for air.
The bad news is does the flapper door work well enough, i.e., enough temp rise. My guess is you could not certify it:
FAR part 23.1093 - Induction system icing protection.
(a) Reciprocating engines. Each reciprocating engine air induction system must have means to prevent and eliminate icing.
Unless this is done by other means, it must be shown that, in air free of visible moisture at a temperature of 30 ?F. --
(1) Each airplane with sea level engines using conventional venturi carburetors has a preheater that can provide a heat rise
of 90 ?F. with the engines at 75 percent of maximum continuous power;
There are 6 parts to this section, the above is the prime one for a sea level (non-turbo) engine with a carb and carb heat.
I doubt the little stove pipe device Van has on the cross over will raise the heat up 90F, but may help a little.
Again INSTALL carb heat if you have a Carb. If you were going to fly IFR in visible moisture in near freezing temps as part of your routine missions, I would use a dedicated heat muff for carb heat. Of course a carb air temp gage would be handy.
Put the carb heat door in, use it, check it (don't rush it) and be aware of the dew point spread. I don't have a rule of thumb except for the standard induction ice chart, showing probability against temp vs. dew point temp. Google: "carb ice" or "induction ice" airplane, to get a chart.
To compensate for Van's weak carb heat, use it sooner than later, more often and keep it on longer. Once the engine starts to choke from ice you may be screwed. BTW those fancy EGT gages may give you the first indication of ice in cruise. Again like the run-up, if in doubt pull it on. Watch RPM or MAP as appropriate for a change. Obviously you will get an initial MAP or RPM change from using alternate air, but watch it after that initial drop. As ice melts the RPM or MAP may increase. After the carb heat has beenon for a short period, turn heat off and note the RPM or MAP again for overall change from the start point. If you watch you will see you often will see small amount increase of RPM or MAP, indicating carb ice from time to time you may have not been aware of before.
You have to look to see it.
How to live with carb ice (read if bored and at own risk of involuntary drowsiness )
Here is the deal even with a weak carb heat system it is way better than none at all. Second you need to get carb heat on and early if it is likely or suspected. Consider this a limitation to respect and observe. Here is a tip you may or may not know about. As a former practicing CFI I have seen pilots do run-up checks of carb heat that do no good at all. You need pull the carb heat and leave it in for a reasonable period of time, while observing RPM or MAP if you have a constant speed prop. Note any increase in RPM or MAP. Here is the part some miss. Once you turn the carb heat back off note RPM or MAP again. If it has changed, higher than when you started, you likely had melted some ice off you got during taxi. Obviously if you are in Phoenix during the summer, carb ice is not an issue. A carb check can be just a quick functional check in this case. Remember you can have carb ice conditions with ambient temps as high as 23c to 30c with high humidity. Carb icing is most likely at 50%+ humidity from 20 to 90 degrees F. (Some texts give 80% humidity between 40 and 70 degrees.) This applies to RV's and Lycoming engines as well.
Detection: There is no direct way to detect ice except for a LED optical ice detector device like the "Iceman", which uses a LED and photo cel to "see" ice. However many report it is too sensitive, reporting the slightest ice or frost on the sensor. However consider an old fashion Carb Air Temp (CAT) probe and gage. If for any reason to see how effective you carb heat is. My GRT EIS4000 engine monitor uses a (CAT) probe and will give a visual alarm in the critical range. With the CAT you can keep track of actual venturi temp, but it still will not tell you if you have ice. You still need RPM, MAP, EGT and a careful eye. The critical CAT range is +15c to -10c. Some analog CAT gages show caution range as +/-20c and others show a +/-10c range. Again it is just an indirect indicator or possible ice, which is a little more useful than OAT.
Carb ice contributes to many accidents every year across the GA fleet, including several RV's. The problem is the evidence rapidly melts and disappears. The main thing is awareness. Use the darn thing EARLY and be real suspicious and discerning of what the gages are telling you, before, during and after carb heat applications. Also if you fly with Carb heat on below 75% power don't forget to re-lean. As far as taking off with carb heat ON, I would not recommend it. If you get carb ice taking off with full power, assuming it was cleaned out to start with, I would not be flying at all (in a SE recip airplane). The conditions would be severe and you likely could have airframe ice as well (100% humidity and OAT with in +10C of freezing).
Cheers George