Is it possible to prevent methane combining with oxygen?
I doubt that the conditions in an Anaerobic digester (organic acids, ammonia (!), etc) allow algae to grow. If they do, the oxygen they set free will create oxic conditions and stop the AD - Methanogens are obligate anaerobe bacteria.
In nature, Methanogens and Algae inhabit different habitats - methanogens in the mud at the bottom of a swamp, algae (maybe) in the water above.

Processes for separating $\ce{CO2}$ from $\ce{CH4}$ usually work on the $\ce{CO2}$ (absorption in amines or water under high pressure), so it would be hard to pull the $\ce{CH4}$ from the headspace of your vessel - but given the biological points, this is a non-issue.