Adding acid and chlorine one right after the other will produce no adverse result.

Get your pH down now and your Cl will be noticeably more effective.

Do you think the pH is really that urgent right now?
Yes. Lowing pH with pucks is a little too slow for what you need to do. Leave the pucks in there if you like but you need to get your pH in a range you can test. You don't know how high it is.