Can Thraustochytrids such as Schizochytrium do photosynthesis?
I think not. 

from Kingdoms and Domains: An Illustrated Guide to the Phyla of Life on Earth By Lynn Margulis, Michael J Chapman. as found on google books

You will see there are no chloroplasts depicted.  These are eukaryotes and so to do photosynthesis they would need chloroplasts which should be evident.