I've had my transit pass checked now and then on the trolley, but never during SDCC. It's always been too mobbed for an enforcement officer to even work their way through the trolley car. But it could always happen.
If you stick your paper pass in your badge holder, BTW, you may want to seal the top of the holder somehow (I make my clip go through both layers of the holder). Back when I was less careful, my (four day!) pass fell out on the exhibit hall floor. That was painful.
That said, paper may be the best option -- I'd certainly recommend against the mticket app, because you never know when you might end up wanting to take a bus, and it's not as though you get a discount for going trolley-only. Also, a paper ticket may be slightly more convenient than having your ticket on a Compass card -- you have to tap the Compass card on a machine at the trolley stop each time before you board, and with crowds, it can get hard to find or access the machines. I don't have a choice, since I have a monthly pass on a Compass card, but the paper pass (once you obtain it) seems like the easiest option if you're going to ride a lot.
(Also, FYI, a single day pass can be purchased on a bus ($5 if you have a Compass card to load it on, $7 if they have to print you a paper pass) but multi-day passes cannot be purchased on buses.)