As the title says, will I?
Ex: I have PR 5, and suddenly a thousand sites link to me and they all have just PR 0, 1 or 2, will this cause my PR to drop?
PR can only go up when you get a new link pointing to your page. Not down. The effect of links is cumulative. You don't get the average of the links pointing to you. And PR never goes down, even if the link is from a link farm or a bad neighborhood or whatever else Google says is bad. The worst thing that can happen is they pass no PR to you page at all. (If you link back to them then you may be considered part of the bad neighborhood and then suffer penalties from that but that is outside the scope of the question).
This is not a question for here, maybe webmasters.stackexchange.com
But the answer is NO, Google doesn't hold you accountable for the incoming links. (it would be very easy to harm your opponent if so).
EDIT: Just in case. This is unless you link back to them, then, I does affect you.
BTW: PR is not that important any more and is not directly related to incoming links!