You ask 'will it be o.k?'
The biggest point is 'what will happen if you do?'
The main consequences will be : it sounds great and everyone will love it; it will grate and sound horrible and no-one will like it; something in between.
You will not lose a go, or be locked in jail.
Often, the bass notes will reflect the chord at the time, rather than vice versa, which is your proposition. And here, you suggest other chords with that A note contained within.
So, yes, it'll work. It won't be what the listener expects - C > Bb > ? more often does > F. But isn't that one of the points in music. The unexpected. 'I didn't see/hear that coming'. More to the point is - now you're out on a bit of a limb, let's see how you get back home safely.
The biggest criterion is how it sounds - to you and the listener. The 'rules', aka 'theory', as we keep banging on about, will try to explain what's happening, to help future readers. Guidelines, maps, if you like. But if everyone stuck to the well-trodden route, nothing new would ever get discovered.
EDIT: you ask if any chord will fit. Probably not any chord, but certainly any containing that A.