It’s ambiguous, and unfortunately, I would say the stronger case can be made for “no.”
First, some rules quotes:
Touch spells allow you to touch someone as part of the casting of the spell, and touching them may involve an attack, but the thing you are allowed to do is touch, not attack. If the touch happens to be an attack, so be it, but it might not be, and in any event, you aren’t allowed any other non-touch attack.
Smiting Spell “alter[s]” a spell to be discharged as part of a weapon attack instead of a touch. But it says nothing about altering the touch you are ordinarily allowed as part of casting a touch spell to now be a weapon attack. It doesn’t address that touch at all. As discussed in another question, you (probably) can’t even touch the target with the weapon, since you’ve altered the spell effect to be discharged on “strik[ing],” not touch.
Ultimately, getting an extra application of weapon attack damage is not worth a feat, and it’s not worth a spell level. Most of the time, it’s not even worth the lost accuracy—you could allow all touch spells to be delivered with any weapon attack, and allow it to be part of the original casting, and most of the time you’d still be better off touching. So if Smiting Spell is forcing you to pay extra for this effect you probably wouldn’t want even if it was free... it’s probably not worth having.
Note that unarmed strikes can deliver touch spells without any need for any feat beyond Improved Unarmed Strike (see Complete Arcane pg. 73). The tentacle whip symbiont from Eberron Campaign Setting doesn’t even need that, and additionally has a built-in natural poison and 15-ft. continuous reach (per Magic of Eberron pg. 154, a tentacle whip symbiont is approximately worth 8,000 gp, which is a great price for the effect, but of course no one just sells the things, so YMMV on actually acquiring one). These options are vastly superior to Smiting Spell for this purpose.