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 counterspellthe D&D beyond references to counterspell 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).
Manshoon's Simulacrum, Rishaal, Violence, Animated Statue, Miraj Vizann, Bastian Thermandar, Evoker, Kaevja Cynavern, Marta Moonshadow, Azbara Jos, Vajra Safahr, Sylvira Savikas, Rath Modar, Darribeth Meltimer, Turbulence, Counterflux Blastseeker, Alhoon, Preeta Kreepa, Pow Ming, Shedrak of the Eyes, Left Hand of Manshoon, Berlain Shadowdusk, Biomancer, Manshoon, Skeemo Weirdbottle
