Yes, it is possible. No, it is not a good idea.
Alkaline batteries are prone to leaking even if used normally. If you try to recharge them the possibility of them spilling their guts everywhere is greatly increased. So the question is, how much do you value the equipment you plan to use these batteries in?
Some of us have completely abandoned the use of alkaline batteries. As someone has as their tag line on another forum: "Friends don't let friends use alkaline batteries."
Current rechargeable battery technology in the form of Sanyo eneloops or similar products has all but rendered the RAM battery obsolete. Eneloops will work in almost all applications of alkaline batteries, and crucially, they will not leak.
For those odd occasions like clocks where you want to use a disposable battery there are Energizer lithium primary cells. The Energizer Advanced lithium has the same capacity as the Ultimate lithium for 2/3 price and as with the eneloops, they will not leak either.
There is no need to risk leaky alkaline batteries in any of your devices these days.