Yes, they derive from the PIE root sal- . As well e.g. Latin "sal", English "salt", German "Salz". The h as first letter of Welsh "halen" is also found in Ancient Greek "ἅλς" [hals]. (In Modern Greek "αλάτι" [alati] the spiritus asper is not pronounced any more.) The chemical words are taken from the Greek version of sal-
This switch from an original s in onset position to h is usual in Greek. (cf. "ὑπέρ" [hyper] and Latin "super"). In Welsh this occurrs also sometimes. Besides in "halen" it is in "hi" deriving from PIE *sī, English "she" (which still has the s).