A digital will be okay for the first year or two, at most.
A good acoustic piano will have a nice weight to the keys and, as far as I've searched, a digital piano cannot imitate it (And I've tried out Yamaha's Avantgrand N3 pianos which retail at £13,000, absolutely useless for a classical pianist).
The need for the weight keys is essential for the pianists technique. Say, for instance, the teenager takes it seriously and wants to learn. An electric piano will hinder any type of strength in the fingers, which in turn reduces control. If they can play a fast passage cleanly on an electric piano and that's all they've experienced they will more than likely trip up on an acoustic piano.
Another drawback is expression. It is near impossible to get any convincing form of expression out of an electric piano. When playing on an acoustic the pianist will become accustomed to the different vibrations the strings make when different pressure is applied. They'll be able to feel the vibrations of the piano through the pedals and the air, which are quite important things to feel when they get more experienced.
Another major issue with digital pianos is the pedals. Unless you're going for a top of the range digital piano the sustain pedal will simply have an on and off function. The pianist will lack any idea of pedal control. They'll lack the understanding of half pedaling (And it's benefits). Electric pianos which do have a continuous feed on the sustain pedal still do lack somewhat in their affect - I have a silent system fitted on my piano, granted it's extremely useful, it lacks a bit in the sustain.
As a pianist who had to endure 8 years on an electric piano I can tell you it's not worth it. If you have the drive and passion you can perhaps rectify the technical losses when you get an acoustic piano but it's hard work.
You can find second hand pianos extremely cheaply and they can be good quality as the seller either doesn't realise the value or they just need to get rid of it quickly after a downsize. Should you buy a second hand piano also go to test it out to see if it's right for you and bring a piano technician to have a look at it as you don't want to be buying a piano with a cracked soundboard.
Best of luck!