Yes, it will be slower obviously, but virtually all 64bit cards are designed to be backwards compatible with 32bit PCI. There are a couple of disclaimers though. Firstly some motherbords place componants too close behind the PCI slots, so they would foul on the extended connector (or worse short it out, and potentially cause damage to both motherboard and card), Secondly PCI's been though several generations, 5V, 3.3V, etc. There are different keys on the slot, to prevent the wrong card being inserted.
A second issue, is the PCI speed. PCI can be 33Mhz (Most common standard on desktop computers), but it can also be 66Mhz (more common on servers, and 64bit slots. But even 64bit slots can be 33mhz or 66mhz).
Anyway, 'most' cards will automatically negotiate with the motherboard to set the 'best' speed. However it's not 100% guaranteed that a card designed for a 66mhz PCI slot will perform properly at 33mhz.
At the end of the day, unless you short out the card, damage is very unlikely, so why not just plug it in, and check it out. If it works, and its performance is 'acceptable' then you've got no problems.