Hoping to skip that dismantling step
Let me dash that hope first (sorry!) you're going to need to do some dismantling.
You have to do some, and to do a really thorough job you have to take it down to individual pieces. Not doing this (with anything, even something as mechanically simple as a hand plane) is doing a half-assed job of it.
The reason you need to do at least some disassembly is that all rust-removal processes require access to the rust. And nothing can magically reach inside the gap between a nut and its bolt, or any screws and the threaded holes they go into1. Two pieces that only press together tightly can be treated for days or weeks and have the rust between them be completely unaffected.
So to do this properly you need to separate things.
I was wondering if it would be a good idea to submerge the entire machine in electrolysis to remove it in one fell swoop.
No. It won't work, at least not the way you're visualising.
Apart from certain technical difficulties trying to do this on something of this mass, electrolysis has a certain line-of-sight effect between the part and the sacrificial electrode(s). While this problem can be exaggerated by detractors of the method it is undeniably a factor, and it means that internal surfaces, hollows and of course the small gaps I mention above will get little or no rust removal while the externals get clean.
What to do instead?
For something of this size I suggest a molasses bath as a cheap, safe (for you and the rusty object) and effective alternative. Here's how effective:
For large-scale rust removal like this molasses solutions are hard to beat in terms of cost effectiveness. Other than the smell2 the only real downside to this method that I've seen is in the speed. It's slow. But why be in a rush?
As with all rust removal processes it's a very good idea to clean the thing reasonably well before you start. Brush off any loose rust while you're at it. Most important with chemical rust removal is to degrease as much as you can because any significant oily or greasy surface deposits will slow or prevent the chemical from being able to act on the iron and steel.
As with all chemical solutions molasses solutions are more effective at higher concentrations. You'll read various dilutions given online (10:1 and 11:1 seem to be popular) but my experience and that of others has shown it still works far more dilute than this — 20:1, possibly lower. Which is handy for something of the size you're dealing with!
As with all chemical reactions it goes faster at higher temps but it's not vital that the solution be kept warm, a molasses soak does continue to work in the cold. I've had continued results at maybe 2-5°C (35-41°C) on a cold windowsill in an unheated room, however it is noticeably faster in the summer.
It's a relatively slow method at the best of times. For heavy rust deposits think weeks not days.
Your molasses solution can be used many many times before it's exhausted, some even suggest indefinitely. I've never had the chance to test this out myself but I have kept a bath going for over two years and other users report they've had theirs up and running for much longer.
In the US a common source of molasses cheap in bulk is at somewhere like a feed store.
1 If there even is one! Bad rust tends to have closed this gap, which is precisely why rusted bolts and screws are so hard to unscrew (even when they go into wood, where there's no "rust weld" effect).
2 Some people don't mind it so much but it is strong and if you don't care for it will be a little off-putting. But you don't have to be around it much because as soon as the thing is fished out of the solution you'll be moving it to one side and hosing it off.