The pH is specially important for the enzyme which you are using, since it do have a optimal work pH, in that way adjusting the pH would enhance your electrochemical signal. What we do usually is repeat the same experiment in different solution with different pH, usually buffer, since it keeps the pH stable during the experiment.

In generally, enzyme has a optimal pH.  Higher or lower pH will decrease enzyme activity.

As Sergio said, should consider the samples you are work on.

About sensing property of the electrode, the most critical point is the formation of protons during hydrolysis. To avoid it you should use buffer. NAOH should be added to buffer during its preparation

However some buffer have already stable pH

I am using 0.1 M H2SO4 in SDS as supporting electrolyte, should I vary the pH of this solution or should I be using another electrolytes like Phosphate buffer, potassium dihydrogen phosphate buffer (used as electrolyte in some literature)  of varying pH ?

I am not using any enzyme it is just a functionalized electrode with MIP and Gold nano particles.

First question, which one electrochemical method do you apply for measurements? If you use MIP and not use enzyme, wy do you call your system "biosensor"? If there is no enzyme, then my suggestion is to think about ionic strench and inhybitors of MIP recognition. Needed pH can be made by NaOH or H2SO4, but in my experience, 1 mM of NaOH water solution is ca. pH 10 and lower concentrations did'n keep exact pH, e.g. first measurement day of 0.1 mM of NaOH is ca. pH 8, second measurement day pH of the same solution is already 7.5. 

Biosensor does not necessarily mean enzymes but all the biomolecules need a specific pH (antibodies around pH 7.4 or DNA around pH 8). You work with MIP (synthetic antibodies). Probably there is a range of working pH, but usually in electroanalysis if you want to scan the whole pH range, you use Britton Robinson buffers from e.g. 2 to 10, same composition and only varies the pH. This buffer consists of a mixture of acids: acetic acid, phosphoric acid and boric acid, and once you have the mixture of acids, you use NaOH for getting to the pH. For lower pH I use 0.1M H2SO4 and higher 0.1M NaOH.

I am using 0.1 M H2SO4 and 0.8 mM SDS for TC detection (favored in low pH) (PH of the solution is 1.7), Now I would like to increase the pH range up to 5 and see the effect of pH on peak current. If I use buffer the system may not detect any TC as it another system, using NaOH may give a result of effect of NaOH itself rather than pH. May not be a big issue as I can do some hit and trial but if some one has worked on this before and faced similar issue please share.

Thank You