To Bill (the OP) - I did the Meet and Greet on the DT12 tour in the same venue where you'll be seeing them. Assuming things there haven't changed much (and considering what a landmark tour this is), you can bank on there being many people there for the M&G. If you're a sociable person this is a good thing, because you'll all be waiting around for long periods of time while the band does soundcheck and things, so you can talk about the band with fellow fans. If, like me, you're not a sociable person, it's still interesting to hang back and just watch and earwig some of the more obsessive fans who will be there. I can say that for me personally, one of the most interesting parts of the whole experience was seeing what stuff some fans wanted the band to sign, some seriously obscure DT items.
First is the photo with the band, which is pretty self-explanatory. You all line up on one side, get the picture taken, and then wait on the other side for everyone to get through. It took about 20 minutes. Then the band sits at a row of tables and you all shuffle through getting stuff signed (2 items max) and you can have a quick chat with them. Understandably, there's not much time for that part of it because the band's time is short. I saw them on that tour a couple of weeks later in Russia and in Lithuania, where there were only 20 people and about 8 people respectively, so on those occasions it was a proper hang out, with Jordan especially very happy to take lots of pictures on people's phones and cameras. JP gave me a plectrum, and Labrie spoke to me about the Russian language for a while.
The band themselves, at the Manchester gig at least, were a mixed bag in my experience. Myung was the biggest surprise for me, he seemed genuinely appreciative of the fans, offered me his hand during the signing. Petrucci, Rudess and Labrie (especially Labrie) are also cool in that environment (Petrucci always shook the hand of anyone who extended theirs, though it was made clear at the beginning that fist bumps are prefered), and Mangini was a bit stressed out that night because of technical issues at the previous show (written about on here at the time), so he was actually a bit rude, but a couple of weeks later he was a different person. Just an off night for him, we all have them.
Is it worth it? It depends how big a fan of the band you are. I'm pretty rabid, so I didn't think twice about doing a bunch of them (primarily because at that time, the ticket and the M&G were part of the same package, so if you wanted the best seats, you had to buy the Platinum package. I mainly wanted front row seats opposite JP each night). The price is relative, for some it's a lot, for others it's nothing. I think I paid, at that time, 190 pounds for everything, but frankly it was worth it to me to get JP and JR to sign my copy of their Evening With CD (which JP momentarily didn't recognise when I handed it to him), and also to quickly tell them how much their music meant to me.
Finally, I don't know if she's still working for the band, but in 2014 there was a young woman who organised the whole thing, who walked the fans through how it all works and tried to get some 'excitement' going. She's absolutely superb at what she does, very helpful if you have any questions or problems. A shout out to her, if she's around.