Could induction thaw ice?

Induction uses magnetic fields to move free electrons in a regular lattice (ie: a conductor). Ice doesn't have very many free electrons or a regular lattice, so no. It does have a few large ions and protons, but they are at least 1600X more massive, so they don't move much. In this YouTube video, iron filings are dispersed in ice in order to provide a conductive heat sink -- otherwise it would not heat.

An inductive heating device could be used to heat the pipe directly, though.

Something that could heat the ice directly is microwaves. I don't recommend it, however, as there wouldn't be much stopping the energy from bouncing around and heating you!

An non-electronic solution to a similar problem in Canada, which is that mobile homes and cottages can have exposed water or waste (sewage) pipes that can freeze in winter. The majority of this piping is plastic now.

The most common approach is to use a thermostat controlled electric heat "tape", which has a waterproof coated heating element (high resistance wire, such as used in electric blankets) which is based on Joule heating rather than induction.

Ad-hoc solutions could include using hair dyers or heat lamps. Even incandescent light bulbs could be used.

How about a good old fashioned heating blanket? That would use electricity to get hot without having to fish heating coils either in or around the pipe and wouldn’t be as dangerous as playing with a microwave’s magnetron.

Induction from a standard electromagnet wouldn't be able to cause normal water to get hot. If you had something of high enough frequency such as a magnetron you would be able to use dielectric heating to slowly melt the water.