Are you talking about the actual Free Trial (14 days without buying the game and with some extra limits like can't go past level 20)? Or are you talking about the 30 days that comes with purchase of the game, which sometimes also gets referred to as being a free period?

If he's still on a 14 day Free Trial and hasn't yet bought the game, purchasing it to expand the limited Free Trial into a full paid account will wipe out any time remaining on that 14 day trial. If you mean the 30 days that comes with purchase of the game, that's time that's been paid for and he'll get it regardless of when (or if) he adds additional subscription time. Additional subscription time gets added to the end of whatever time he already has.

(Yeah, the last sentence of your first post makes it sound like you mean the later, which makes QuinceTaru's answer right, but to avoid confusion with other players seeing this, I thought I should spell out the distinction, since both get called "Free Trial" at times.)