If you get an email confirming your pending deposit before you've got a confirmation you may also be able to double spend the original transaction allowing for you to mitigate paying extra fees (as the 2 transactions could be replaced by one).
This introduces additional risk without knowing how the back end of the exchange works. There are plenty of places I have sent bitcoin which give you an address and monitor that address for an incoming transaction. As soon as an incoming transaction is detected, they stop monitoring the address and just wait for one (or three, or six, or whatever) confirmations. If you replace your initial deposit with a new transaction, there is a chance that the new transaction is not detected by their system, and then OP will likely have to spend days or even weeks going through the exchange's support team (which are almost universally awful) to get his coins credited to his account. This would only be safe if you are absolutely certain the exchange only gives you a single deposit address and does not change it.
Similarly, if he sends a small amount prior to sending the larger amount and the exchange does change the deposit address, if both transactions are to the same address he will again be faced with the above scenario.