You ask:
if booming blade or green flame blade are counter-spelled, does the attack still go through?
I answer
if booming blade or green flame blade are counter-spelled,
You have discovered that your enemy is a fool. Feast upon them.
The economics of this transaction: your enemy traded a level 3 spell slot for a level 0 slot.
You just won that exchange.
You suckered the enemy into wasting a counterspell on a 0 level spell (cantrip) that you can cast again on the next round, for a 3d level spell slot that is a limited resource. And now, next round, the enemy usually can't counterspell the Hold Person that your cleric is going to throw, or some other spell from level 1 through 9, depending on your tier of play and your team's composition.
Caveat: Enemies with counterspell as an at will ability
It is worth noting that the Aeorian Nullifier (Wildemount) has counterspell at will. I didn't find any others, but a DM could customize a monster to have that spell known for an NPC/Monster that has a 3d level casting slot. Most NPCs will use it with a spell slot (or in the "x / day" style).
@Kirt noted in a comment that ...
A powerful NPC in a certain official adventure has counterspell as a third level spell, can cast spells of up to third level at-will, and can use a legendary action to cast any of their at-will spells.
Enemies with counterspell as a spell slot
I discovered in reading through the D&D beyond references to dispel magic that a variety of NPCs or Monsters have counterspell as a listed spell. The Evoker and Abjurer (VGtM), or the Mage and Arcanaloth (MM), or Githyanki Gish(MtoF) are straight up NPCs and monsters; most of the others are in published adventures so I'll keep them behind a spoiler. Note: any caster with a 3d level spell might have it subbed in for a listed one, if the DM customizes NPCs. (I customize spells known occasionally if I feel the generic NPCs' thematics are 'off' for the story).
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