Sure they could and pilots make mistakes too (yes really)
This is just discussion - Since there is no systematic exclusion of the possibility you have to assume that the possibility of "cleared to" actions may be in conflict or that pilots may be flying or taxiing in a manner other than cleared and thus be in conflict with a properly cleared approach. The possibilities multiply when visibility is restricted. At SNA one evening when I was flying home from work when 45 knot winds and blowing dust favored the normally unused runways 1L and 1R, I was cleared to land on 1R, an airliner was cleared to land on 1L and a 737 was cleared to taxi south on Alpha. At SNA it is not all that uncommon for someone to overshoot turn and be in conflict with traffic for the other runway. That was not the case on this night however, the problem was the 737 missed the taxiway and taxied south on 19L. I did a very tight turn to final to beat the landing airliner (and his wake turbulence) so the conflict with the 737 was fairly close and there was very little time for the controller (a different one for 1L and 1R as well as Ground) to recognize the conflict in the midst of working the rest of the incoming traffic for 1R and issue "04L go around". Fortunately, I was doing my job, recognized the conflict and was already on the power and setting up for the abort. Another potential conflict that can occur where you would not be aware of a potential conflict is when different controllers or frequencies are being used for different traffic situations (approach directions, patterns, etc.) and an aircraft is cleared to land on a crossing runway but hold short of the other runway - but doesn't. The possibilities at uncontrolled multiple runway airports with instrument approaches and normal VFR operations are limitless. Controllers often exercise cutting edge separation judgement based on experience with specific situations and specific pilots/airplanes. For example at SNA I returned from work every day for 15 years or so and I would often be cleared to land on 19R between two airliners because the system was close to saturation and they trusted me to avoid conflict. I can tell you that the flying demands for compliance were sometimes very very demanding and the trailing airliners were a bit tense, as was I, but we scratch each others back and make it work for everyone. Occassionally there is the "taxi into position and hold" situation like the tragic one at LAX a few years ago. I think you are right to wonder about the possibilities and the rules and legal implementation will not preclude conflicting traffic on multiple runway airports. My rule is expect the system to minimize the conflicts but be alert for them anyway.
