The short answer is, maybe. Liquid carbon is not actually liquid carbon at all. It's glutaraldehyde, an algaecide. It's used in the medical field to sterilize equipment. When introduced into our aquariums they produce a VERY small amount of CO2 and companies like Seachem claim that you can "Use as an alternative to CO2 injection or in addition to it"... more like, in addition.
So then why do I give it a "maybe" and not "YES, you should be dumping this stuff in by the gallon"? Well, point blank, there really isn't a substitution for CO2 injection. That is always going to provide the most benefit to a planted aquarium. However, this still is really good at killing the algae that presents itself in tanks that do not inject CO2, which is Black Beard Algae, or BBA. BBA most commonly presents itself when the water column runs out of available CO2. To simply put it, you may need to inject more CO2 into your tank. You can read more about BBA here.
Increasing your CO2 injection rate, or making sure you're achieving proper CO2 saturation levels should always be the first thing you do to make sure it doesn't come back, then you can address getting rid of the BBA. A product like Seachem Excel will kill the BBA turning it red over the course of a few days. You can also spot treat BBA-ridden leaves and hardscape. That does work a little better but we can't always drain our tanks. Once it's dead and turned red, you can brush it away. It's pretty stubborn to get off sometimes. I generally use a new toothbrush to bush off the hardscape, glass or wood, a wire brush for rocks, or a scrub pad for glass and or silicone corners. Once you've removed it from the tank, and if your CO2 injection is where it needs to be, you can stop dosing it.
Here is a little video that does into more detail about "liquid CO2" products: