Let me preface this by reaffirming that I am not a lawyer and that what follows is a guess based on my limited understanding of software licensing. If you need a real lawyer, talk to a real lawyer, and if you're just looking to understand the issue theoretically, use the score my answer gets to gauge whether it's wisdom or nonsense.
In general - a software's license will enumerate which rights are explicitly granted to licensee(s) and which are explicitly reserved by the licensor(s). It may very well be possible there are also rights on which the license is silent. Let's assume the right to remove the bit of code that forces end users to accept the EULA and subsequently distribute this software appears in each of these three categories and what the implications are.
Suppose the right to do this is explicitly granted to licensees. That is, there is an explicit right granted which, reasonably construed, allows the licensee to remove the bit of code and redistribute the result, and there is no more specific right explicitly reserved by the licensor to this effect. Then licensees are free to remove the check and redistribute the software. Note - I am not sure whether this means users who receive the software have a right to violate the terms of the EULA; the party who removed the code might be the liable party in that the EULA was misrepresented to the end user (the end user may simply be made to stop using the software against the terms of the EULA). This seems analogous to the situation where someone steals some property and passes it off to a third party - the third party doesn't get to keep the property but doesn't (necessarily) go to jail. Note that in this case it's not the removal of the EULA agreement section, per se, from the code that is problematic - it is the failure to adequately convey the terms of the license. Of course, if the license grant the right for licensees to redistribute the software under a different license, any violation by the end user would be against the relicensor, not the original licensor.
Suppose the right to do this is explicitly reserved by the original licensor. Then any licensee who modifies the program in such a way has already violated the terms of the license, even if when distributing the modified copy he makes sure end users accept the terms of the EULA.
Suppose now that the original license is silent on this question, or that there is a roughly equal balance of rights granted vs. rights reserved. It might be possible to construe EULAs as being similar to a contract of adhesion in that one side unilaterally dictates the terms and the other party either accepts or rejects the agreement on a "take it or leave it" basis. If this thinking were to be accepted, then "close calls" would usually go against the party who drafted the license, i.e., the party modifying the EULA would be free to do so and redistribute it. Note that this isn't necessarily a defense against not taking all reasonable precautions to ensure that the end user is aware of and accepts the EULA under which the licensor originally distributed the EULA.