Can I wear a diamond pendant with a 925 silver chain?

Sure you can!
But you will have to get the chain polished much more frequently because silver oxidizes pretty quickly.
But because it is a pendant, which usually oxidizes much slower than say a silver ring, you should only need it polished every couple of months to keep it bright white in color.
Most diamond pendants are placed on white gold chains because they discolor over a much longer period, and the fact yellow gold isn’t “in style” right now. Eventually you’ll need it Rhodium plated again, but it will be years before you need this service.
In the short run you’d save some money because obviously silver is much cheaper than gold, but if you want it to last longer and looker better over time, I’d recommend purchasing a nicer chain.
Especially if it’s holding a diamond!