PAs definitely have a lot of responsibility... It's not all bad, you would be responsible for ordering which will be rough at first and takes a little time to get down. You will also be looked upon to maintain service scores and freshness and working closely with TL to come up with action plans for reaching/maintaining all the metrics. You will get very familiar with running an area/department and the tools available to maximize sales, profit, team work, and guest experience.
Like insiteful said, if you prove yourself as a PA being a TL isn't a big step and it will surely teach you a lot and give you talking points for the interview process. I say go for it!!