I don't think so. There are several limiting issues going on
- You only have 1 pcie slot and thats for your GPU.
- you are pcie Gen 1. I do not know if the current m.2 drives & adapters will negotiate down to a gen1 pcie link.
- i'm sure your chipset hasn't and will not receive a bios update to support m.2 if it needs one. It definitely would need one to support an nvme m.2 drive but maybe not for a sata/ahci m.2
Since your system is so old I would suggest you stick to a sata SSD for greater compatibility. Your system uses sata2 so you should be able to run a sata3 ssd, just dont expect to see those speeds as it wills till be limited to sata 2. This shouldnt be much of a concern. I have an old sata2 motherbd running an htpc and its the...