Clearing using finings during racking prior to bottling - will there still be enough yeast for second fermentation?

I am taking the opportunity to use the current situation to get brewing again. I'm only using kits at the moment, but plan to move to next stages soon. I currently have a Festival kit of Old Suffolk ale in primary and will be bottling early next week. I'd like to remove as much of the trub from the bottles as possible, and will probably use finings in the secondary before adding the priming sugar and bottling. My question is two fold.

Firstly, if the finings work, won't I be left with some new trub in the bottom of the second bin, which will get mixed in when adding the sugar?

Secondly, if I get around that, will there be enough 'good' yeast in the beer to execute a successful second fermentation (this question was asked, but in a filtering context, not finings)