Maybe very rarely, but it's usually almost entirely one or the other. If the seam is upright and it "swings", it's almost certainly not going to spin.
Also an over-spinning ball, which is what a "finger-spinner who bowls with the seam consistent" is doing, is not likely to swing but it will get a lot of drift.
Starfighter would probably have more scientific insights
Lol I'd like to have more scientific insights but frankly I can't be arsed arguing with Cricketweb's Walter Mitty. Pretty sure I've been over this before.
@cnerd123 is right the distinction between swing and drift is more modern. This means we can't be sure by which mechanism the ball moved in the air. The same goes with movement off the pitch. 'Spin' vs 'cut' is more of a methodological distinction (Spofforth defined it as, spin you twist your fingers and or wrist, cut you just push down one side of the ball). They both put spin on the ball, along some axis. Wisden happily praises Ted McDonald, who we have footage to at least show he was *not slow*, for the amount of spin he put on the ball.
We will never know exactly what orientation Barnes released the ball in, and so how he moved the ball in the air. But when his contemporaries say he did what he did, noting how unusual it was, it's a fair bet the movement existed, regardless of how it happened.
And no, overspinning the ball won't get a lot of drift. I had a very lengthy post typed up that I completed on drift, it's saved somewhere on my computer. But most people don't know it's the spinning-top like competent of the spin that gets the drift, not the sidespin or overspin.
And I've played with someone who could consistently swing and spin the ball. He only bowled about 100 km/h and with the seam upright but oriented about 40°. Not the most favourable angle, but the ball did still swing a bit and if the pitch was at all soft or worn the ball would rip away from the left handers, he was very good at getting them out as they played towards the leg side with the swing.