Simple answer: NO.
Here is why.A 64 bit processor must be used in a motherboard built for the larger memory space. Because the advantage of 64 bit is mostly the larger
address space available. (Many laptops already had
a 64 bit data bus.)
Laptops are not made to be updated like desktops can be.
The notable exception is a laptop that allows a video card to be added.
Here is how a laptop could be upgraded.(Follow the links in the above web page.)
IMO, you may consider selling your laptop and getting a new one. A lot of improvements have been made in the past 9 or ten years after you got your laptop. For one, the batteries are now better and now fast laptops use less power.. And, of course, they run either 32 bit or 64 bit software.
How good it would be if our computers were easier to upgrade.Hope this helps.