No. Not because of a strength issue, but because dimmensional lumber just moves too much from season to season. 1/4" ply is often luan, which is quite unstabile just the moisture form thinset can cause it to delaminate.
Is the first layer wood planks? Those can stay, but you need at least 1/2" c-faced or better ply on top of the planks to isolate you from the wood. The ply needs exposure I glue (not to glue the ply to the subfloor, to make the ply).
Then, you need some sort of isolation membrane or cbu, installed properly (thinset under then screws or nails), then you can tile.
If you want a long-lasting tile install, you also need to verify that the joists are okay.
The floor you have is plenty stiff between the joists (but would move too much in the seasons)...now you need to determine the strength of the joists.
Check out
www.johnbridge.com for tiling info.