No it isn't. Anything capable of running any Java application suits.
Recieving IOTA requires almost no CPU cycles.

However... in practise things are more complicated. Some day you might want to be able to spend those IOTA, and that requires POW work to be done on your sending site. There are no miners who mine blocks for a small fee or block reward. That laptop should have some GPU. Intel i3 dualcore with onchip graphics suited me so far, besides some issues on occasion. Tried on a single core lacking any graphic hardware, attaching an empty new adress onto the tangle, ninty minutes runtime: No success.


Brainstorming: However "mining" could become a future bussiness? Service gets PGP signed message containing recipient address, percentage amount of fees to be gained, tangle explorer source address and private key wrapped inside additional PGP envelope that only this very service can decode. After two days (or arbitrary timeout) everybody could see if they initiated the transaction and played honest on fees. Lacks complete trustlessness.

Naw engineering overkill again, trying to force some "IOTA mining bussiness" into the scenario. It's doable replacing client sided POW work with Fee Payments, but unneeded.