A contract just requires an agreement between some parties. Signatures only matter to the extent that they serve as proof of an agreement. You can't go into court and say "yes, I agreed to the contract, but I never signed it." That's a losing argument.

You can, on the other hand, totally go into court and argue "Yes I signed the contract, but I never agreed to it!" That's obviously not an easy argument to make, and you'll need to give a pretty compelling argument if you want a shot at winning, but fundamentally, the signature is just evidence of an agreement, not some legal requirement.

So, clicking 'accept' on a EULA is solidly in a gray area. Everyone knows that no one reads the terms before clicking, so if the EULA has you signing away your first born, you can totally argue "yeah, I clicked the EULA, but I didn't agree to THAT" and probably win. On the other hand, clicking the EULA does mean that you're on notice that you've agreed to something. If the EULA is just the standard stuff that you'd expect to find in it, then a court is likely to enforce the terms.