Rabbits should be possible. But Guinea Pigs and dormice are likely to be too expensive.
Chickens are relatively easy to mechanically pluck, and apparently they're mechanically gutted, too.
Mammals would likely have to be skinned, which would be a trickier task - unless the fur could be singed off?
In any case, eviscerating a 5 lb chicken is apparently doable and quite economic. If you had large scale production of rabbits, building machinery to gut a 5 lb rabbit ought to work fine.
As I say, rabbits should be doable.
But mechanically eviscerating a 1 lb guinea pig or a 2 oz dormouse would likely cost almost as much per animal as for a chicken.
Making the process expensive for guinea pigs, and prohibitively so for dormice.
Of course, the Romans ate them whole, didn't they? Heads and bones and guts and all. Ick.
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OK edible dormice are like 4.5 oz, not 2
And guinea pigs can easily be over 2 lb.
Still.
(Edit. Chicken 2-2.5 kg, guinea pig 1 kg, dormouse 125g, ballpark, in real units)
If dormice were eaten whole, they might be price competitive. But not on a rotisserie, I'm sure. Probably sold in oil or honey or something in tins or jars.