I've done that trip several times on / in some pretty awful machinery and yes, you won't have a problem getting there and back in a month. The problem is likely to be whether the driving is seen as an integral part of the trip or just a means of getting from one place to another. If it's the latter then (particularly with teens) you're likely to hear many increasingly vocal variations on the theme of "are we there yet?".

You might keep younger teens distracted by videos, games, music etc but older ones are going to get extremely bored (and then fractious) if they're just dumped in the back of the car while the adults make all the decisions. By 18/19 I and many friends of similar age were doing these trips for ourselves and, one generation on, my children were also arranging their own travels in their late teens. If you can make the travelling something they have a stake in it's likely to make the miles pass easier.

From about the age of five until she started travelling herself my daughter absolutely hated long car journeys. We did try to get down to southern Italy once but had to give up when she became refused to leave an overnight campsite near Pisa. She wanted to go home and that was it. My wife spent the next three days doing sing-along nursery rhymes with her while I drove and our son sulked in the back because she'd ruined his holiday. By the time we got back we needed another holiday!