No, any recent computer (< 10 years old) will do it, as long as it is connected to internet and you launch the Bitcoin daemon or wallet.
I would recommend a SSD as a must these days. The difference from HDD is notable. Also be sure to have a decent amount of RAM. Anything less than 8 GB and you might struggle. Many computers from around 8 years ago still had 4 GB. 8GB minimum is a must. On the CPU front, I've tried with a 10 year old quadcore and it works, given that the hard disk and ram part are covered. Internet wise you also must have decent bandwith and upload speed decent enough to help other peers.