I sent some XMR soon after downloading the gui client (unknowingly) before completion of the daemon synchronization... Will my XMR appear eventually or are they lost?
It is a common misconception to those new to cryptocurrencies that the coins are "stored" in a wallet. In fact, the coins are stored on the blockchain. They are always there, waiting to be accessed and spent. Your wallet, at its core, is simply a key holder. Your wallet holds the key(s) that allow you to spend your coins.
The answer is no, your coins are not lost forever. Your wallet's public address was used to generate a transaction that consists (among other things) of an output that only your wallet knows belongs to it (because of your wallet's private viewkey), and only your wallet can spend (because of your wallet's private spendkey). (Nearly all cryptocurrencies only have one private key. Monero is an exception to this.)
Your wallet needs to sync with a fully synced node. The GUI can be used to connect to and sync with a remote node. Many people do this (at the potential expense of some privacy). Usually (but not always), the node you connect to will be in sync with the blockchain; and when your wallet syncs with it, the coins sent to it will appear. The GUI can also basically act as its own node, in which case it will download the blockchain and verify that it is legitimate. Once the blockchain sync is complete, your wallet will sync, and you'll see your coins.
In some instances, the blockchain will be fully synced, and the wallet will fully sync, but the coins don't show up. This is rare, but it happens. Generally, having the wallet rescan the blockchain will remedy that. But also, make sure you didn't accidentally set up a new wallet with a new seed, because then your address will be different, and the wallet keys will be different, so your new wallet won't be able to find the transaction output destined for the old wallet.