Ungrounded Outlets

Older house. 1948. Replacing original two prong outlets that are most definitely not grounded even if I run a wire to the clamp screw in the back of the box. I’m pretty sure it’s up to code if I put in a GFCI, but should I go ahead and put in a ground wire to the screw in the back of the box anyway, even if it’s not an actual ground, or should I leave that ground wire out completely?