Dell build their pc's using some custom fit components - often centred around the HSF / Fan - which is frequently fitted with a plastic shroud so that the fan not only cools the cpu but also acts as an exhaust fan.
Then there is also the ill fated / supported BTX format / motherboard design.
I would start by checking whihc mobo is installed - download "CPUz" and it will If they have used a standard ATX board then you might be able to fit the HSF / Freezer 7 - but it might mean the venting for exhaust will need to be removed
Dell computers use BTX design, which involves a BTX HSF system that blows air from the front directly to the rear.
99.99% of aftermarket CPU coolers use ATK designs. So no, it will not be compatible.
However, BTX designs are generally more efficent than ATX designs, so a BTX heatsinkfan will be better than a stock or cheap ATX heatsinkfan.
Clean out your current heatsink and see if it improves your temperatures. If you were planning to buy the AC Freezer7 Pro for overclocking, note that Dell motherboards usually have their BIOS locked so you can't overclock.