Is give an answer to a different question. I have Opera 7.21, Opera 6.05, and Internet Explorer installed on my PC. I can have all three of them loading pages at the same time. Naturally, this slows down page loading on any one of them, if the other is also busy, but it doesn't seem to produce any conflicts, not even if I access the same web page at more or less the same time.
So I think the answer is, try it and see. If it doesn't work at all, come back and tell us what happens.