Yes. You stop receiving rewards from the moment you request an unbond.
Please note that once you request an unbond, you will need to wait 20 days for the tokens to be released.
The reason for that is rooted in the security mechanism of staking - if stakers are able to unbond immediately, they can perform a so-called front-running attack on a potential slash penalty and therefore compromise security. The default pool, Tom, does not have slashing, but the same security measures apply across the whole staking system.
Once your tokens are released after the 20-day period, you will be able to re-stake your tokens if you wish - you will simply have to do it as if you are staking for the first time.
If you request Unbond and have unclaimed rewards, please note you'd have to still manually claim your rewards (and you don't have to wait the 20 day period to claim them). Simply click on CLAIM and sign all pending transactions to do so.