Pseudo Random Number Generator and Propagation delay
Your example is quite primitive compared to PRSG's with more entropy and better characteristics, but you need to define more than just latency as all buffers add latency.



PRNG's of order n all have one state out of the maximal length of the possible 2^n states that is invalid. 

Using XOR vs XNOR allows you to choose that invalid state, so you MUST avoid it for the initial condition. Namely $00 for XOR and $FF for XNOR where the generator appears stuck. 

You chose something other than this invalid state as the initial condition such as a certain seed value or a SET or RESET.

The latency is always the n value of the bits in the register. It is normally used with a large n >7 so the DC component is negligible or the offset between the total number of  1's and 0's for a long frame of bits between resyncs to eliminate the DC component.  

Without a special seed, otherwise, it is impossible to balance this but then with say 2^19, does it matter?

The other thing to consider in latency is the entropy of previous bits in each burst or frame of data bits if it is not continuous.

Normally for each packet of data random generators are used for some channel requirement. If you need security or fast decoding or more error detection or correction , some use Chinese Remainder Theorem methods.