Whether you play with or without nails on the right hand, you can play on gut strings. If you play without nails, you do not necessarily want the varnished e' b and g because the stroke of flesh across the varnished string can create a barely audible squeak. It is important to keep your left hand dry by cultivating a poised and relaxed mental state while you are playing. Moisture from the left hand will wear the gut strings much more than playing with nails on the right hand.
Can you tune the gut strings up to a'=440? You can, if you do so gradually, playing chromatic scales along the length of the e' string as you near the high pitch. But of course a greater tension on that e' string on a 650mm scale guitar will wear the string more quickly, and gut strings can and do break. If the string breaks at the nut, it is likely that the groove in the nut has not been properly chamfered along the front edge. This is a common problem because with nylon strings there is no need to chamfer the forward edge of the nut.
You might consider tuning slightly lower that a=440hz. See my article 'A Brief History of Pitch Standards.' I favor pitch standard in use for much of the 19th century; a'=435, 'diapason normal.'