Some commercial refill liquids may contain up to 5% or possibly 10% alcohol (data taken from an analysis of a Ruyan
e-liquid seen on Health NZ website). However it seems doubtful this amount could have any observable effect even on a child, considering the tiny total quantity consumed.
Another matter is whether or not consumption of tiny quantities of alcohol might be a bad idea for those intending to cease use.
Yet another genuine issue is that people may not want to consume alcohol at all. You would need to obtain an assurance from the Supplier that none is present. This would be difficult in some cases as the regional distributor may not know the contents.
Alcohol might be present in very small quantities in a flavoring (the term 'extract' when applied specifically and correctly to a plant extract means it has an alcohol base); and alcohol has probably been used as the thinning additive in some '100% VG' liquids instead of DW, distilled water.
So yes, it can be in there - it's extremely unlikely to have any noticeable physical effect in such small quantities - nobody knows if it might be best to avoid for some people - and those who definitely want to avoid it might have trouble doing so.