I know of no USBC rule to make this scenario illegal. so, I would assume that this is legal per USBC rules; but the league could adopt a rule disallowing it. 

You probably can not take away the ability to replace a bowler, especially for the scenario of an injury or departure for an emergency of some sort.  but I would think you could adopt a rule similar to baseball; once you have been replaced, you are done and can not return for that league night.

Perfectly legal

Commonly Asked Questions – Rule 104a.
104a/1 May a captain change the lineup from game to game?
Yes. Unless it is a match point league or there is a league rule to the contrary, a captain may
change the lineup from one game to the next. Rule 106b, Item 1, states that once a game
has started, no changes to the order can be made after the start of a game. The rule does not
place a restriction on making changes during a series. A captain may change the order of the
players, replace a substitute with a regular member or make any other lineup change from one game to the next.