I recently purchased some bitcoins, which were sent via coinapult to my cell phone. I received a text for the amount with a link to an online wallet (apparently not a true wallet but just an account within a larger wallet). I would like to have my own wallet. I’ve downloaded the bitcoin wallet program (for windows) from this website. (bitcoin-qt) version 0.6.2-win32. When I open this program it claims to be “synchronizing with network” a certain number of “blocks”. In the “received coins” tab is listed an address. Using my coinapult via the link provided on my smartphone I sent a bitcoin to the listed address. However I see no evidence it was received. Do I need to wait for the synchronizing process to complete to send bitcoins to this wallet?
Using the default client (which it appears you are) transactions received while the client is online will usually appear immediately but transactions which occur while the client is offline will not appear until the block containing them is downloaded. Based on your description this appears to be what has happened, so your transaction should show up whenever that particular block downloads.
You could also try punching your address into http://blockchain.info and you should be able to see your transaction as well as what block contains it.
You can send Bitcoins to a wallet even without being synchronised, but you will most likely only see them appear once you do get synchronised. If everything goes well (it should), your address will be credited and the record will be stored in the block chain, allowing you to retrieve it upon synchronisation.