Technically yes but it would be generally worse at self-sustaining scalability - you need to construct more greenhouses, keep the higher exposed surface area of water from evaporating, and find a sequestering use for that algae.

Non-biodegrading bioplastic made with renewable eneegy could technically work for that role but more plastic waste isn't approved of for obvious reasons.

In addition to capturing carbon, forests (of native tree species) provide many ecosystem services, including fresh water retention in the land, food and habitat for other species, shading of the ground, etc that a greenhouse full of algae would be challenged to provide. Most of the carbon stored in a forest is subterranean and increases significantly over time.

I don't know, are you familiar with carbon capture rates for algae? It's a good point and one to explore: trees/plants vs. algae for carbon capture. If you could make a modular system of tiles (say 10' x 10') comprised of carbon capturing method of choice (algae pools, trees), would it make sense to install these on buildings in cities (or anywhere, but suggest cities because that is certainly where such things do not exist at scale anymore) (then consider fabrication and maintenance costs)? I have no idea what the solution is to the carbon capture problem, but increases opportunities for carbon capture seems like a high level solution.