June is a good time to go - long daylight hours and less crowded I would be tempted to just let them get on with it themselves learning to rely on themselves in a new environment whilst on a journey will be an invaluable experience including doing the research. They will have a great time!
I think it’s a great idea.... what a memorable summer for them. There are a lot of towns and villages on the route but I think you (or better still they!) would need to plan ahead and book accommodation as they won’t be the only people doing it in June. B&Bs in North Cornwall can be expensive - so make use of hostels where possible. Also remember to budget for food and drink which they will need plenty of - it’s quite a strenuous walk. The path is easy to follow and stunningly beautiful but has a lot of ups and downs. Keeping properly hydrated (not beer!), and out of the sun as much as possible is a necessity that can’t be hammered home hard enough to a pair of 18 year olds. Dehydration and sunstroke are serious and very real risks in this windy and shadeless environment.
Sounds great. Get him a copy of the Trailblazers coastpath book, brilliantly written and very helpful maps. The oliver's Cornish coastpath website (http://oliverscornwall.co.uk/oliverscornishcoastpath.htm) is also useful. Have done most of the Cornish path now over the last few years, but we tend to stay in posh-ish hotel these days, so can't help much on that score. There are some lovely hostels/pubs though. Even in June, I would book ahead in places like Padstow and especially St Ives.