Yes of course if swordsmanship aspect is kept intact...Though it would lose some of its charm without the releases, but even so, Bleach has other cool things besides a Zanpakutou release...And it's not only just the Zanpakutou which defines the swordsmanship aspect of the series...For instance, some quincies have swordsmanship aspects without the Zanpakutou...Yhwach, Hashwalth, Gerard, Quilge, etc., and fullbringers like Tsukishima too...So in case of Shinigami, losing of inner-world aspect of Zanpakutou in case of Ichigo, and losing other aspects like imbuing part of the soul into the sword and the spirits having their own mind and body aspects, they might develop some other abilities if the concept of imbuing the part of their soul is replaced by some other means perhaps developed by SRDI instead of a concept of blank asauchi by amalgamation of souls.
So in my imagination, if the medium(imbuing the part of their soul into a sword) is kept intact but the form changes(concept of asauchi) besides the concept of the weider's spirit having a shape, body, mind and is replaced by something else(a different theme or a concept), then it would be fine for me...Even without that, it would be still fine to me, but would lose some of its charm to some extent...