I saw this at a couple of AAA games this year. It did slow the game down a bit. The players (batter and catcher) had a pretty good idea when the calls were wrong, and they appealed frequently. Each time took about 10-15 seconds, so it was a like an old-school batter's time out, probably about once per half inning. At some point it made me wonder why the umps were calling balls and strikes at all.
The worst part was they sometimes appealed high-leverage calls, just because "why not?" So you'd get these big calls like an inning-ending strike three with men on base, but then you have to wait 10 seconds for confirmation. It took the excitement out of that play for sure. Instead of cheering for the pitcher's great ptich, you are cheering for the robo-ump confirming the call.
If any of you are college basketball fans, we've got this awful situation now where every exciting play in the last 2 minutes has to be reviewed. It kills the vibe. I wonder if, for TV viewers, they could tape-delay around all this stuff. Just cut the reviews out and have the commentator catch us up as the action starts again.