Apparently not - I asked two of them, and they said it'd work fine, except that there'd be frequency drift. How much this affects the entire circuit, I have no idea.
This is the first wireless course I've taken (building circuits). I understand the theory, but never having experience piecing together components doesn't help. Looking up transmitters on google probably isn't the best idea either - Half the designs are probably just as bad (I'm not saying this because I'm lazy and don't want to search, but I'm sure there are so many different variations, that pin-pointing the best solution isn't really a good option). Plus, I think with this circuit, they are just trying to get me to understand the basics.. just transmit FM - this isn't production quality.