Can beta D-glucose be present hydrolysate after hydrolysis of cellulose and how can it be converted into alpha D-glucose?
In aqueous solution, $\alpha$-D-glucose and $\beta$-D-glucose equilibrate. So glucose derived from aqueous acid hydrolysis of cellulose will eventually become an equilibrium mixture of α and β. 

A 2006 paper goes into great detail on the kinetics and thermodynamics of the interconversion (in water).  They say: 


  At 30 °C, the rate constants for ring closing toward α-pyranose and β-pyranose are 0.044 s−1 and 0.072 s−1, respectively.


Keep in mind those figures don't include the effect of acid catalysis, and are incomplete without rate constants for the formation of the ring-open aldehyde from the two different pyranoses.  But they should give you a rough sense of how quickly the process occurs.  A later figure in the same paper shows that it takes roughly 12,000 seconds or 3.3 hrs for nearly complete (~90%) relaxation to equilibrium.

Also see chemistry.stackexchange.com/a/7311/13184 for more information.