We bought a bargain Laura Ashley sofa off eBay not realising the fabric is silk. And supposedly not to be washed in the machine. I did it anyway and they were absolutely fine on a 30 degree cycle. I air dried them rather than using the tumble drier though. If it's synthetic fabric it will definitely be ok OP, just don't wash hot.
Yes, it makes it a lot easier to get them on when they are a little damp to get the fit nice and tight. If I leave them to dry out its a bloody nightmare to get them to fit correctly, lots of heaving and huffing and puffing!
Mine come with metal screw things that you put through the fabric into the body of the sofas to keep the shape.
I used to wash the Tetrad loose covers at full heat twice a year because it was a white sofa, and replace them just before they were completely dry. No shrinkage problem at all, but eventually the armrest wore to a tattered shred. Now relocated to child's bedroom with a blanket covering the worn area, but it's still quite white, if not pristine.
You’re not supposed to do it unless rhey are marked washable, it ruins the fire protection safety material stuff it’s treated with. You should get an upholstery cleaner person in. They usually do carpets also, won’t cost much and you keep the safety stuff intact.