I'm pretty sure that it's worded so that it's just for the one game. This can result in a hefty GC sink in my opinion (especially if it's a secret weapon and gets thrown out on the first drive) and makes choosing one just for a single match fairly ridiculous.
We have a house rule in our league that the GC cost is for the entire season and no duplicates are allowed. This usually means that they're only affordable towards the end of the season where the team would've managed until on their own merits and have players with (hopefully) similar stats and abilities.