Update regarding the Booming Blade errata (6/9/21):
The Booming Blade errata adds one change relevant to this answer: the weapon used as part of the melee attack must be worth at least 1 sp.
Regarding Thunder Gauntlets, the weapon for Booming Blade would be "your armored fist". So the question (for your DM, probably) is, how much is your armored fist worth?
If you verify your gauntlets/gloves are worth at least a silver, the original answer is still good.
Original answer below:
The description of the Booming Blade cantrip says (SCAG, p. 142; emphasis mine):
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range, otherwise the spell fails. On a hit, the target suffers the attack's normal effects, and it becomes sheathed in booming energy until the start of your next turn.
Yes, you can use Thunder Gauntlets as part of Booming Blade
This is because Booming Blade requires a melee attack with a weapon, and Thunder Gauntlets states:
Your armored fists each count as a simple melee weapon
Yes, you would get the debuff effect from Thunder Gauntlets
The spell effect states that the target takes the normal effects of the attack, which includes both the damage and the distracting pulse.