Your couple's match status is part of your ERAS Profile, and as such can be changed at any time.
Will programs see a couple applying as a positive? Hard to say -- depends on the program and the couple.
If there is a small program, let's say 2-3 slots, and a couple applies, the couple would take most/all of the spots. PD's may be happy with this, and may not. If one person needs an LOA for something, the other may need one also. Or, what happens if one of the couple is struggling in the program -- it could be very uncomfortable for all, and it's possible that both could leave. On the other hand, if all works out it can be a great situation.
If a program has lots of slots, then the problems above fade away and there really is no issue.
The other issue raised is what to do if the couple are at two different "levels" on the rank list. Let's say one is really good, and the other is average. The PD could rank them on the ROL in their appropriate spots, but might lose the really good person if they didn't go down to the middle one. They could move the middle person up to the top. Or they could move the top person down to the middle. Or, split the difference. There is no answer here -- each program will do something different.
You can "stealth" couples match. Nothing stops you from participating in the NRMP couples match and not tell anyone. You simply leave it off your application, and interview on different days.