Chemically, both PG and glycerin are "alcohols" but I'm sure the OP was not talking about chemical classification, but rather about the presence of ethanol - the drinking alcohol, and what is commonly referred to as alcohol in common parlance. In that respect, no - neither PG nor VG should be considered related to alcohol in a practical manner.
As said, juice may contain small amounts of ethanol added for two purposes. It is a necessary solvent in certain flavorings, and it is sometimes used to "thin" 100% glycerin bases. The amount is always small and probably there is little chance of either intoxication or detection by a police screening device. It cannot really be more than very little because of the type of throat hit alcohol would give - I once accidentaly vaped a little VG and a lot of vodka while experimenting with cleaning atties and it brought tears to my eyes.
It dawned on me that your concern might be religious, in which case -- just ask the vendors. However, some might not be 100% able to say what is in the flavorings they use. A lot of menthol out there uses alcohol as a solvent, so do a lot of tobacco extracted flavorings, but there is no hard and fast rule!