Once you fire missiles from a stealth airplane, you give away information just from the bay doors opening. if it was purely a one on one dogfight, the Rafale would probably be too preoccupied with incoming missiles to do much, but if it had wingmen, they might collect enough targeting data.
It's hard to discuss how a real "fair" scenario would unfold, because air-to-air combat is uncommon, these planes aren't likely to fight each other, & there are too many variables: 1 on 1? 2 on 2? With AWACS? How near? Is the F-35 carrying missiles externally? What are their trajectories?
All of those I listed probably play a role in whether the team flying Rafales would see the F-35s in the second or two the bay doors were open & be able to track them & return fire. I assume the AMRAAMs would be very visible on IR, at least giving an area for a narrow-field IR search.
Yes there are infinite variables that would come into play and this is why it’s so hard to come to any conclusions based on one event in one excercise.