It probably uses a switching DC power supply. They vary in quality and robustness, but in theory, a good one will take power off of
the AC when it needs it and not care too much about the quality of the power. There is a pedal generator that outputs 120 DC (yes,
DC), and most switching power supplies work fine with it.
That said, if the microcontroler's memory that stores user settings could get messed up from being under powered, so a UPS might
help. But this should be very rare. Computers have a "power good" signal that lets the mainboard know when it is safe to start,
but cheap DC power adapters do not have anything like this. Ideally, the clock should get all of the current and voltage that it
needs, or nothing at all for at least a few seconds so that the device fully discharges and can resume cleanly. Depending on what
happens to that memory and how it is used, it may just act glitchy until you adjust its settings again, or it may need more work to
clear out the bad data.
Personally, I avoid surge protectors that are rated in joules. They use MOVs which produce a short circuit when the power goes to
high. They damage themselves each time this happens. The problem is that the damage can cause them to short at lower voltages;
sometimes down to voltages that are normal and cause them to overheat and be a hazard. Joules is a ratting of energy, and a
lightning strike that enters via the mains (as opposed to a direct building strike) is only going to be so much, so the Tripp Lite
is probably going to be plenty. Depending on the joules rating and how often you get lighting strikes, replace your surge
protectors every 5-10 years to avoid a fire hazard.
The surge protectors that are not rated in joules usually cost more than $300 USD, and can limit the current that your appliance can
draw (not a problem for a clock), but anything with a compressor might be stressed. A cheaper solution may be to get a switching
power supply that can also take 240V AC. Its design should accommodate a small surge without any irregularity going to your clock.