All Part 135 companies will conduct a check of your FAA records prior to hire so trying to evade any discussion on the matter with your perspective employer at the time of the interview will only come back to haunt you later when you are asked to explain.
Most companies,USFS,CDF and OAS have an application question "have you ever had your licence suspended or revoked in the last 5 years?" so, being anything but upfront will only make matters worse.
The severity of any suspension will carry some weight on your hireability. The worst case being Drugs, Alcohol related suspensions. As for Insurance their (insurance) concern would be accident related incidents, but may well include Drugs and Alcohol now.
You cannot bury your head in the sand and hope noboby finds out, so my advice is to be very up front during the interview (when it becomes evident they are interested in you), let them know your records will show a suspension and explain why and how the suspension came about.
Better to not be selected during the interview process than fired (released) during initial training because you failed to disclose the suspension.
As a former CP I would not rule out the possibility of employing an individual just because he screwed up, I would have concerns if I was left to find out through a record search and the seriousness of the suspension. Afterall if you failed to be up front with me at the start of your job what makes me think you are arn't going to cover up other incidents down the road ie Drinking, Drugs,Over Torque, Temp. The list goes on.
One last thought on this. CP's talk to each other, we work in a small industry and you would be suprized how many people, know people, who know people. I only say that because as your posts states this was a CFI/Student discussion which makes me believe you are both relitively new to our industry.
Hopefully this subject is based on "enquiring minds want to know" rather than facing an existing problem. If its the EMWTK, welcome to the fraternity and we all hope you both have uneventfull yet rewarding careers. If its the latter, well you may have an uphill struggle getting that first job following the suspension, be honest and hope they like you. Remember your candid openness can also be seen as you have accepted your punishment and will continue to be open and forthright making you an asset to the company.