I would say, no they do not. My 9mm 24/7 Pro and .45 24/7 OSS have been kept Cocked/Loaded with a Round in the Chamber, for extended periods of time, with no problems with their Striker Springs. Have not heard of any such problems on Glocks or Springfield XD's, either. Not a problem with 1911's kept Cocked and Locked for extended periods of time, either. In my opinion, Striker Springs will only wear out with full cycling, not compression.
As preventive maintenance, I would replace Magazine, Striker and Recoil Springs every 10,000 rounds, whether they need it or not. But that's just me!