Is possible to perform algebric operation with bitwise operations in PDM domain?
Yes, this is sort of possible.   While PDM signals are full of high-frequency noise, at lower frequencies the "density" domain is limited to signals representing values from -1.0 thru +1.0.   This makes it difficult to implement true addition/subtraction since 1+1 exceeds the range of possible outputs, however if the output signal is scaled back into the allowable range, so averages like 1/2(A+B) and 1/2(A-B) can be calculated by multiplexing the two bitstreams into a single output stream (at twice the bitrate).   

The best explanation of this I've seen was in a series of five articles titled "Signal Processing in the Density Domain" published in 2011 by Dave Van Ess in Electronic Design magazine.   The web copies of these articles exist but the equations and figures from the original versions seem corrupted by the web's evolution over time.   I'll include this link to the finale, Part V which wraps up how addition/subtraction and multiplication work.    

While not easy, the missing figures can be retrieved from the internet wayback machine.