DGP - for many UPS systems, that is exactly how it works.
There are 'switching' UPS systems, such as Micro describes, more expensive - but I am not sold on those as being better. The idea behind those is that the battery will last longer.
I stick with the older non-switching technologies from APC and Belkin - both tried and true for me through even direct lightening strkes within 50 feet of the systems.
Micro - THAT is the damage from which UPS systems can protect and surge protectors can NOT.
As to 'over current and under current' (more precisely - over-voltage and under-voltage which RESULT in over current or over current dependent upon the resistance loading) from the basic power grid - Under Voltage is what causes the most damage to 'motorized' electrics. Slight under-voltage can burn a motor out in a heart beat - while the same percentage over-voltage can actually help the motor run a bit more efficiently. It is the heat buildup from over-work with under voltage that causes the damage. From the issues of over and under voltage (and thus, accompanying current) - surge protectors don't do a damn thing. They can't. There may be a few surge protectors out there with zener diode clipping circuits for cutting higher voltage - but, that isn't worth a whole hell of a lot.
As I said before, surge protectors aren't worth a whole heckuva lot. At best, they can help suppress the minor transients that occur in normal everyday power grid distribution switching - but that's about it. From the extreme (1,000 volt +) spikes that occur due to lightning strikes; UPS systems are the only things that provide real protection.
Micro has a decent lower cutoff limit for the size of UPS systems - 750VA - anything smaller really are just toys. Mine run from 1500 VA to a bit over 3-4k VA. Anything larger than that you are into the 'commercial' arena.
Overhead Power Lines - those are great antennae for picking up/generating spikes inductively from Lightning strikes for miles and miles. The higher the 'population' density becomes - the more the 'power' from/on power lines is 'filtered' (parallel circuits and their effects) - by hundreds and thousands of little 'filters' (ie household taps and the household electronics). That is why, in RURAL AREAS, such as DGP's and what my area used to be - Lightning storms cause a hell of a lot more damage to electronics.

Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good ...