i transferred coins to my wallet, but the wallet hasn't finished syncing with the network as yet, so the coins have not reflected. Is this something i need to be concerned about? Do i just wait for it to finish and then see if they appear? I did use the address the wallet gave me.
Assuming you sent the amount to the correct address you have nothing to worry about. This is expected for a wallet that has to download and verify the whole blockchain. Other wallets use SPV that only verifies transactions for your addresses and thus they do not have to download the whole blockchain. Examples of SPV wallets for the desktop are Multibit and Electrum.
After syncing you will see the balance reflected but you could also immediately check if the coins arrived to your address correctly with a block explorer. E.g. go to Blockchain.info or BlockExplorer and search for your address: you will see the amount on that address, the number of confirmations, etc.