No, you can't install CFW directly. You will get a corrupted error. Just faced this throwing a 1TB in mine.
What you're going to have to do is find the HFW firmware that's 4.88. Make sure the controller gets unplugged as soon as you start flashing (the ps3 reads that first for some reason)...
Here's the situation. I got a PS3 CECH 2001A used and it was on 4.86. Couldn't activate it because it wasn't on 4.88. Jailbroke it and put Evilnat on it. Got the 80023017 error trying to log into the PSN to activate the console. I've disabled syscalls. No dice. Downgraded to rebug trying...