A Soldier will usually reenlist 3-6 months prior to their ETS. Prior to the reenlistment process your contract is processed. Once you sign the contract you are in a binding agreement and your new period of enlistment starts on the day you reenlist. Therefore it is highly unlikely that a Soldier reenlisting could simply ETS as the ETS date would most likely be at least a month in the future.
If you desire to ETS the best process would be not to reenlist and simply ETS with terminal or transition leave. The specifics of this leave process can be found in AR 600-8-10. You can find more information on the reenlistment process in AR 601-280 or by speaking with your BN REUP NCO.