do you still get the recogntion of you have discovered the system in solo mode?
Yes. Solo mode is the same as open mode, except, as it happens, you never meet any other CMDRs. I do all my playing, including exploration, in open, and very rarely see another CMDR anyway. Certainly on my last 15,000 LY trip I saw exactly none, and I am out on another, longer, one, and have not met any thus far. Unless I hit the very rare meeting out in deep space, that means the only likelihood of meeting one is in the last few LY of the return journey.