GRP (glass fibre reinforced plastic) has been around a long time, so it's durability is well established. It's been used to re-line lead valleys - over the top of the existing lead. In fact, on newer houses, GRP valleys are used all the time instead of lead.
I guess you mean resin & glassfibre mat? Rather like the outdated "Turnerising" system where plastic net is spread over the slates, and covered in liquid bitumen.
A right messy job, Tambo, I have to say. Apart from that, your main problem is with the verges. That is, the side (gable) verges, and the bottom fascia/gutter line. I can't see how they can be finished neatly without the stuff looking ragged.
To answer your question: it'll last at least as long as any traditional roof covering. No storm damage likely either. The slates will be held firm.
Also, it'll completely remove the benefit of crossflow roof ventilation, although that is probably not a problem with an outbuilding.
Even with colour pigment added to the resin, it's not going to look good. A bit like a Lego house ;o)
I'll stick my neck out and say that carefully re-nailing the existing slates would not cost squillions.... possibly not a lot more than GRP. Slates re-nailed properly always look good. I'll use modern materials whenever I can, but in some cases ............................ ;o)