Nope. A good surge protector should last right up until it blows. MOVs are pretty much a standard and like MedB says. MOVs will go bad after a long time, or if subjected to poor environmental conditions. I've seen some really good ones that use SCRs that will trip at a very specific threshold and shut the system down quite fast, faster than MOVs if engineered right. Swinging Chokes used to be an old fashioned way to regulate minor surges back when the utilities weren't quite so reliable.

Sounds to me like your computer repair place is trying to sell you something, or maybe they are only experienced with low end products.

Most consumer designed "UPS" systems are actually SPS's, or stand-by power supplies. A true UPS is not going to be that inexpensive, and not really suitable for most residential applications. With a true UPS, the battery source is dedicated to the supply output. With an SPS, the batteries are charged and then held out of the supply circuit unless the Primary source goes down, in which case the control circuitry switches to battery supply quicker than most equipment would feel the dropout (electrolytics hold the output up long enough for the switchover to kick in, so long as the load isn't excessive). We're talking milliseconds, since none of the system relies on a mechanical switch over (it used to be relay controlled, but solid state has become reliable and beefy enough to handle it all at much faster switch times). SPS systems also provide decent protection from surges, but not the isolation that a true UPS does.