Swapping external drives for Time Machine

I read a number of earlier discussions, but didn't find one that quite directly addressed my question. Please consider the following scenario:

iMac and MacBook Time Machine backups are stored on a single network drive (attached to an Airport Extreme).

That drive is simply ejected and stored off-site.

Second drive takes the place of the first.

Can first drive simply be reconnected and used to restore the complete system without major issues?

Are there othe