Tl;dr moves called by Sleep Talk are affected by Guts, and so is Snore prior to Gen IV. If you're interested in the calcs, keep reading.
Sleep Talk isn't a damaging move, so it isn't affected by Guts. However, a physical move called through Sleep Talk will have its damage boosted by Guts:
0 Atk Guts Ursaring Tackle vs. 0 HP / 0 Def Abra: 289-342 (151.3 - 179%) -- guaranteed OHKO
This calculation is shown when "Asleep" is selected as the status condition in Pokemon Showdown's Damage Calculator. Compare this to when no status condition is selected:
0 Atk Ursaring Tackle vs. 0 HP / 0 Def Abra: 193-228 (101 - 119.3%) -- guaranteed OHKO
This proves that being asleep procs Guts.
As for Snore, it's a special move in recent gens -- it won't ever be boosted by Guts. However, we can go back to Generation III, when it was a physical move instead. From here, we can carry out the standard calculations.
0 Atk Guts Ursaring Snore vs. 0 HP / 0 Def Abra: 290-342 (151.8 - 179%) -- guaranteed OHKO
Compared to no status condition selected:
0 Atk Ursaring Snore vs. 0 HP / 0 Def Abra: 193-228 (101 - 119.3%) -- guaranteed OHKO
Thus, Snore does receive boosted damage from Guts.
It is important to note that Guts boosts the Attack stat, and not the damage of moves. In other words, when a move is "boosted" by Guts, it simply does more damage because of Guts' boost to Attack, rather than because of any change in a move's power.
