You may, just be aware of couple possible issues:

- not reaching min. required deposit amount (some exchanges may keep cumulate individual small deposits till you reach it ...  but some can just seize it )

- some exchanges may have sort of expiration time for deposit addies
(e.g at Kraken, I believe you can have only 5 active addies ... generating another one makes the oldest expired ... I'm not sure what happens if you send funds to such addy  )

- some exchanges may not allow receiving funds from gambling sources (e.g. coinbase) ... so participating in gambling sig. may lead to account suspension (if they are able to track down the source)

- there is no guarantee the address will be active forever (usually after some major security incident/update a brand new addies may be generated  )

It's always better to check exchange TOS to avoid possible complications or complete loss.