Yes, it will work. PCI-Express are backward compatible. Just that it will run on PCI-E 2.0 speed but it already have enough bandwidth so, don't worry about the bottleneck issue from the slot.
Just to be clear, u r refering to PCI-E and not the old PCI isn't it coz Radeon HD 7850 only come in PCI-E flavour and not PCI.
If u r not sure what type of PCI u have, post your motherboard make and model so that ppl can check for u.