I’ve done it before, there’s the added layer off faff in having to get the turbo, table, laptop, extension lead etc out every time, but it works just as well. With the added bonus that the noise of the turbo/fan isn’t reverberating around a small room so it all feels a bit calmer.
You do still need a fan though which looks a bit bonkers outside. And music at gym levels may be a bit anti-social.
Depends how crowded you house is, but doing it outside is no less faff than doing it inside and putting it away each time, except the bike doesn’t need to be spotless (and wheel on turbos tend to result the rear tyre spreading a stripe of rubber particles along the carpet and wall). As long as you can store it somewhere (which is the same inside or outside) then mines been setup in the living room, kitchen, spare rooms and bedrooms of various places I’ve lived, the turbo just gets folded up and slid under the bed, stairs, behind the sofa or wherever and the bike wheeled back to the shed.