Yes. What Delta does is its own business and doesn't affect UA. It's not like you might lose your citizenship in some countries if you swear allegiance to another one. (That doesn't happen as much as it used to, either.) It's just as if you earned your UA status, then flew enough on DL to earn theirs.

(That happened to me when AA comped me Platinum several years back to get me to switch from DL. It worked, I didn't fly Delta much any more, but I didn't lose my status and had some DL elite level for a while after that based on dropping just one level per year.)