Well you can… but I wouldn’t. And here’s why.
DIRECTV remotes are really efficient with their battery use. Not only that, the newer ones will actually give you an on-screen warning when the battery is low. You won’t see that warning from year to year if you’re using good alkaline or lithium batteries, but rechargeable batteries don’t last as long. It might actually be more annoying to use rechargeables than it is to just change the batteries every couple of years when they need changing.
If you’re committed to preserving the environment (good for you!) you can certainly use rechargeable batteries but then of course you will have to remove them to recharge them every couple of months and that could mean that either you need to have other batteries around or another whole remote. Newer DIRECTV receivers and DVRs are notoriously harder and harder to control without a remote and with a Genie client… no remote means no control at all. So how environmentally responsible is it to have more batteries or more remotes just so you can use rechargeables?
Don’t get me wrong… use rechargeables when you can, but maybe this isn’t the best application for them.