Does Marth's Falchion Buffs boost Gronblade?

NO. Note that Only buffs from hones and fortify and now tactic skills boost gronblade. Marth's falchion upgrade works in a way but only the Atk part of his falchion boosting upgrade works and the others don't.\

Basically (Hones, Fortifies, Tactic skills and Rally skills Works) and (Spurs and drives don't)

Only buffs that work before an attack work (note the blue numbers on units stats before you atk) on blade tomes. Stats gained "during battle" like drives, spurs, goad, etc. dont work.

They don't apply to Blade tomes, but his Falchion has great synergy with Owl tomes. Having him stand next to an Owl tome user is an auto +4 to all stats. You can take it further by putting spurs on his C slot and S slot. You can take it even further by giving Marth and the Owl tome user an ally support. You can then take it EVEN further by giving the Owl tome user a Bond A skill.

Take for example my setup feature Marth and Mae.

2 (Owl) + 2 (Falchion) + 2 (Support) + 4 (Spur Atk Seal) + 5 (Atk/Spd Bond) = +15 Attack

2 (Owl) + 2 (Falchion) + 2 (Support) + 5 (Atk/Spd Bond) = +11 Speed

2 (Owl) + 2 (Falchion) + 2 (Support) + 3 (Spur Def/Res) = +9 Defense

2 (Owl) + 2 (Falchion) + 2 (Support) + 3 (Spur Def/Res) = 9 Resistance

Altogether that's 44 points of raw stats just by having Marth stand next to someone. A budget version of this without the Bond skill isn't even that hard to accomplish either and still very effective.