Chosen Solution

I have an older HP Splitx2 touch laptop and would like to add a SSD to it. Is that possible?

Yes - go for it! And as soon as it is possible - your laptop will be grateful. Since SSD discs work on SATA interface you can swap your Hard Drive to a new one (2.5” required). You can also dismount your DVD Rom and buy an pocket for external disc. But it should be picket for your laptop model.