The entire area is approximately four feet by four feet. the joist are 2 inches by 9 inches by 11 feet
My experience is no, too much bounce. Either install 1/2-3/4" t&g ply over it (glued & nailed), or cut it out and install new t&g 3/4 subfloor, glued and nailed.
Also consider your floor joist width and span. In this question, that's undetermined.
In either case, then you can install 1/2" cement board.
Virtually all brands specify minimum 5/8" plywood or OSB as a base.
I have to say, if it was my house and there were significant challenges related to plywood installation (plank removal difficult, heigh problem with plywood over plank, etc.) I might consider mortaring and screwing it down without the plywood if and only if the plank subfloor was very sturdy (no flex/bounce/deflection when jumped up and down on) and very flat.
fasten any loose planks and flatten (plane, sand, chisel) any planks that are not level
1/2 inch - 3/4 inch exterior rated plywood or osb, screwed down to the planks the screws should avoid hitting the joists
thinset applied with 1/4 inch x 1/4 inch trowel applied on top of the plywood/osb
1/2 inch cement backer board on top of the thinset and screwed in just after the thinset is applied. it's O.K. to walk on the cement board before the thinset sets