As long as they did not snooker you with the nominated free ball itself it's a legal shot.
If they nominated the yellow as their free ball and then the yellow winds up snookering you it's a foul.
Personally I think if you're playing more than 2 players you should forget about playing snookers and use a lift rule. ie. you can't be snookered when you come to the table, the blocking ball is removed for the shot and replaced after you hit. That's just easier all around when playing recreational snooker and will save you lots of arguments
First off, to the OP: I am so happy to find out about someone else trying to just have fun with the game using non-standard rules. Of course, the proper Rules of Snooker are written for two players head-to-head or for two teams in a consistent playing order. If your situation differs from that, then you are outside standard rules so you are free to be (and I encourage you to be) creative in determining your own rules of play.
Sickpotter, I have heard of this "lift rule" before (but not called that....no specific name for it, it was just described to me) in association with some forms of American Snooker. I commend the creativity of the rule but I do not agree with it in principle and I am not aware of any precedent for adopting this rule no matter the circumstance. Just like the law, often new rules (new law) will be piggy-backed on existing, similar situations. That said, I have a different rule that I would suggest to Rob(E) to play in frames of more than two players. In fact, for fun, I think this is a great rule even in two player games. It forces pots, not snookers so much. My group is closed minded and they all seem to think they are the next Ronnie O'Sullivan so I cannot get them to do anything but what is written down in the Official Rules. Which is kind of funny when you lose a frame by giving up 20 or 30 points on a Foul and a Miss that was quite clearly a fluke since six or eight object balls were in motion on the shot and one of them just HAPPENED to come to a stop blocking off the White ball. In fact, I suspect about three-quarters of the snookers laid against me are the results of flukes though the opponent will never own up to it.
Anyway, for Rob(E), the custom rule that I suggest that you invoke in this circumstance is something I learned playing three way pub snooker and the idea is very simple. It is just called All Out Offence and all that means is that there is no benefit at all laying a snooker on the next striker because the incoming player ALWAYS has the option of putting the previous player back on the table for the shot he left. (See how it piggy-backs....it is just based on how you can put the opponent back in after a foul. Only difference is in AAO, the incoming striker can always put the outgoing striker back in, hence, it does you no good at all to lay a snooker whether by accident or on purpose because the next striker will just put you back in to play the bad shot anyway.)
Now, AAO can be played in a few ways. You can play that all the way to the end, final Black ball, or any colour you wish to name (for instance, AAO to Blue). Or if you see some strategic value in laying snookers, most common is AAO to Colours (or "AAO to Yellow"...same thing) and that means that you play AAO as long as Reds are on the table (still applies to the pot of Colour following the last Red), but upon the very first shot at the Yellow in the final colour sequence, from that point forward, standard Rules apply so laying snookers is permissible. So it is important that all the players in the frame know what the rule is but this is very easily agreed upon by stating it before the breakoff, i.e., "All Out Offense to Yellow", or "All Out Offense to Blue" or whatever else the players may want to agree to. Simple. And you need a custom rule for the point that someone needs snookers....say someone needs snookers and there is still two Reds left. The options are: 1) play it to the agreed Rule even if snookers are required to win (i.e., if it is AAO to Yellow, you still can't snooker with the Reds but try to make up your points from Yellow onward), 2) throw the AAO out the window and if someone needs snookers, then they are allowed to play for snookers, or 3) hey, it is just a frame for fun anyway so if someone gets to a point of needing snookers, end it and rack up a new frame. Entirely up to you. If you are actually playing for something, say a fiver per player or whatever, best is to say that if someone reaches the point of requiring snookers to win, then they are just out and the remaining players continue. If you do it this way, you are best to play AAO to Black (or "AAO to the end") so if the frame gets to the point that everyone needs snookers except one person, then obviously, that player wins the frame and wins the money. Rack 'em.
So I agree in principle with Sickpotter but I recommend a different alternate rule as being easier to understand, easier to actually execute (how do you get the ball back where it belongs for the "lift rule"? no simple, accurate way), and I think more fun throughout the game. I am fan of properly played defense, but at low level snooker (which is most of us), accidental safety and snookers (which is often most of it) is really just a pain in the backside and not much fun in my opinion.