No, but they'll only cross train you where it makes sense. They won't cross train you in the backroom while your FA.
What you might want to do is express interest in going above in beyond in your core roll and learn some new tasks that could be applied to your original work center. Example, getting cross trained as a cart attendant or cashier. You could pick up a CA shift and then be able to backup FA when it gets busy. Or if it's particularly slow in FA and there is double coverage, you could break away and help out the CA or help ring up guests. Eventually you might be able to push to get salesfloor shifts under the same guise....you could be the only person on the salesfloor that could backup FA. Everybody else on the salesfloor can backup cashier, but you could ALSO backup FA. You might be able to push for it via that angle, especially if you have a particularly busy FA.
But you'll have to show you can excel in your current work center. If you're mediocre in FA, the thought process will be that you'll be mediocre on the salesfloor...and it wouldn't be worth it to put in the extra effort for a mediocre team member. Be enthusiastic, be great with guests, have a cheerful personality that would translate to a great salesfloor TM, and you might be able to make the transition.