Dear Anand,

Yes there are different groups of microalgae that are capable to ferment cellulosic biomass for their growth, such as Aurantiochytrium sp. or other "fungal-like" protists like Pythium irregulare (capable to ferment plant roots).

I don't know in detail for CMC but there are many microalgae that can do this (search for extremophile algae too)

Thank you so much Giovanni Luca Russo for your inputs.

I DONT KNOW IF IT CAN HELPS YOU Thierry Lebeau · Jean-Michel Robert Diatom cultivation and biotechnologically relevant products. Part I: Cultivation at various scales

***At higher aeration velocities, a hydrodynamic stress appeared, although damage to algal cells was not shown. To overcome this drawback, supplementation of the microalgal culture medium with carboxymethyl cellulose (CMC, a modifier of interfacial properties) at a concentration of at least 0.2% (by weight) was shown to protect the algal cells against aeration-induced hydrodynamic stress. The CMC had a purely physical protective effect and no physiological effect on the algal cells (Camacho et al. 2001).****