No. In fact to truly protect your PC you need to pul the power from the wall and and lines from a router as lightning can travel through any lines in your home (phone, coax, cat5e).
A ups would help in the event of a surprise outage, provided it's large enough. It would allow you to safely shutdown the pc, not really continue using it for more than 5-10min at most (not under gaming loads, high power consumption). If turning off the switch on the power strip, it shouldn't require a ups. Only because it sounds like you're turning off/switching off the entire pc during storms/lightning to begin with. Unplugging from the wall wouldn't change anything other than prevent a lightning strike from damaging the pc. If you didn't need a ups when switching off the main strip power, why would unplugging it mean you'd need one?
personally i'd unplug everything, unscrew the outlets, remove the receptacles, pull out all of the wiring, and sell the house.
Or use a surge protector that actually does protect from lightning. These are completely different from items that plug into the wall. Since plug-in (power strip or UPS) protectors do not claim to protect from surges that typically cause damage.
All appliances already have robust protection. Your concern is a rare transient (maybe once every seven years) that can overwhelm that existing and more robust protection. For over 100 years, only a properly earthed 'whole house' protector has been that solution. No protector does protection. A protector is effective only if it connects low impedance (ie less than 10 feet) to the earthing electrodes. Neither power strip nor UPS have that required feature.
That Ankway does not even claim to provide that protection.
Nobody can disconnect in sufficient time. It any appliance needs that protection, then every appliance needs that protection - including clocks, furnace, dishwasher, dimmer switches, GFCIs. What most needs protection if a surge exists? Smoke detectors. Only solution that protects everything and does protect even from lightning is the well proven 'whole house' solution. Since destructive surges often occur long before anyone even thinks about unplugging. If anything needs protection, then everything (ie LED bulbs) need that protection.