So, I KNOW this isn't 'canon' because it wasn't a true Capcom game (licensed, not created by) buuuut...
Rockman and Forte: Challenger from the Future has fascinated me for a while with its plotline, as there are elements of it that could be said to bridge the Classic and X series (with some mental straining, of course.)
I haven't been able to find a script online at all, but I did find the Wonderswan ending screens translated:
http://www.vgmuseum.com/end/ws/a/rf.htm (Forte)
http://www.vgmuseum.com/end/ws/a/rfr.htm (Rockman)
Rockman Shadow (who ISN'T Quint, believe it or not) says in Rock's ending that "It would be a lie to say that Wily continues his evil ways in the future. With the destruction of Quint, I was the only robot left." I suppose if you want to be a smartass, you can say that Zero wasn't a 'robot' but... I find this statement very interesting- even if it's just because I'm developing the Wily-redemption concept here and there... XDD
RS goes on to say "In the future, no one could stop me, but I traveled back in time so I could find someone that could defeat me. I didn't expect another robot like me to be created..."
At the end of both endings, Rockman Shadow's spirit visibly leaves his body...
Conflating this with the revamped line in IHX about X "having a soul that is nearly human" and all the cyber-elves of the Zero line, I'd say it's pretty safe to confirm that Reploids and bioroids do have tangible souls, not just programmed consciousnesses.
What became of Rockman Shadow's spirit?
Edit to add for permanent reference:
http://www.wikiknowledge.net/wiki/Rockman_&_Forte:_Challenger_from_the_Future#Mega_ManThe Wikiknowledge page for R&F: C blows away wikipedia's page for great justice. XD