As far as I'm concerned, low CPU, RAM, and disk storage would just make the Database slower. Reading and writing to the database could be noticeably slower.
Database servers are software. Some are able to take advantage of multi-threading processors (or multiple processors, either), some are not. Disk usage will depend on the size of the data. RAM usage will depend on how many users are connecting simultaneously, and what kinds of operations they are doing. Commercial database servers have beefed up hardware and operating systems, but you can run a simple database almost anywhere for a few users and get away with much smaller specs. So unfortunately, the answer is, "it depends" on several different details.
