My own experience:
I got my two budgerigars FIRST. About 3 months later I fell in love with my Sunny and brought her home. This was a year or so before we all went work-from-home. AFTER i got Sunny i was reading about how they need yay-much human-interaction time, etc. Well i did the best I could with before-and-after work time. ALSO i made sure the cages were next to each other. BIG cages, with lots of toys and activities. Chunks of veggies attached to the cage walls before I head to work, etc.
I made a point of turning on Radio each day before leaving. CLASSICAL station -- because, although I don't hate classical, exactly, I will Always switch it to something else if I am listening for a short while. SO this let birdies know I was leaving For The Day. (One day I came home early -- upset stomach -- and it was clear from Sunny's cute-but-confused reaction that due to the music she did NOT expect me!)
Anyway my point here -- I had my two budgies first BUT this Really Really worked for me. The petstore budgies are not-really tame, and as long as you have a pair, they don't really Require lots of human interaction. They ARE social, though. And although my Sunny ACTS like they are invisible (really! she still does this!) -- nonetheless they are there, chirping away, interacting, and so she Knows she is Not Alone even if I am gone.
Now -- IF you WANT another Larger-than-budgie bird, that is a good reason to get one. BUT. As others point out -- they Might OR Might Not get along, you COULD lose your bond, and now you have TWO birds that Require human interaction.
OR if you want some company for your bird, don't mind more mess, but DON"T want the Risk - you could get a pair of petstore budgies* -- or finches -- or a canary, to keep near your conure. To give your GCC some company without necessarily risking your GCC-relationship. And whether your GCC loves or hates its bird-companions, they Will still BE COMPANY, in an adjacent cage, when you are gone for the day. Your GCC will not be "all alone" all day.
(*ps I am NOT suggesting budgies as any sort of throwaway bird, nor any sort of lesser-than bird. BUT if you get Two (or more) from petstore, and provide Good, Large, well-enriched cage, and care for them well, ----then you can have as much or little "relationship" with them as you want to attempt, and they can still be Equally Happy with their lives. Petstore budgies, non-hand-tamed, do not REQUIRE daily one-to-one human interaction for their happiness.)