Does the use of power surge protector makes up for the lack of the ground pin?
No it does not. The ground or earth connection is a safety feature. The ground pin connects to the (metal) case of a product and/or any other parts the user (you) could touch. If for whatever reason those metal parts try to become live (connect to mains due to a fault) then it cannot as it is grounded. In a modern installation the RCD would trip and switch off the mains for your safety.
It is very likely that your equipment is double isolated and has this logo:
In this case even when it has a ground connection, it does not strictly need to be connected.
In rooms with carpet or wood floors it can be assumed that even a live voltage on the case will not immediately electrocute the user because of the (electrical) insulating properties of said carpet or wood. So then often the mains sockets have no ground connection.
Having said that, in an office environment the ground is really required and not having it is not a very good idea.
The surge protector only tries to block voltage spikes on the mains. Most modern equipment also has similar circuitry build-in already so in my opinion, surge protectors are a waste of money.
Some people claim surge protectors claim that these protect when lightning strikes. That might be true if the lightning strikes reasonably far away but then the build-in protection can handle that as well.
When lightning really strikes close by on your mains wires, no surge protectors can protect your equipment agains that. There are examples where even the mains wiring evaporated after a lightning strike. Not much a surge protector can do against that kind of force.