I worked in a Benefits Dept for 6 years.
The first question you should ask when discussing benefits with your prospective employer is if the plan has a pre-existing condition clause at all. It's a very common question and you should be able to ask them without having to dislose why you want to know. Even if it does have a pre-existing condition clause, it usually means that you would not be able to to have medical care related to that condition covered by the insurance for a certain amount of time (maybe 6-12 months).
If you are terribly concerned about HR/co-workers finding out about your condition, you might want to check to see if the health insurance plan is "self-insured" or "self-funded". This means that when you make your insurance payments the company keeps the money in a big pool and uses it to pay the insurance claims/medical bills (thus they would see your medical bills). Given that you will be at a small company it is highly unlikely that it will have a "self-funded" plan since there are so few people. If one person had an expensive illness (for example: cancer treatment) the pool of money would be drained quickly. If you are familiar with the name of the insurance company then it most likely is not a self-funded/insured plan.
With a private insurer, the HR person might get a usage report (7 office visits, 25 blood tests etc). I don't know how detailed they are (varies by company) but they should not have any names or personal indicators on them.
One benefit you might want to be cautious with if you are concerned about coworkers finding out about your HSV is the Medical Spending Account. This is a way you can save paying taxes on out of pocket medical expenses by having money deducted from your pay check each pay period and put into the MSA account. You get the money back when you submit receipts for medical bills you paid. You can save 40% in taxes by doing this! But, if this is processed by the HR/benefits person they would see the receipt (ie for the copay for your Valtrex). It is possible that they might outsource the administration of this type of plan too.
I currently work in an office of 15 people. The health insurance is not self-funded. I get Valtrex all the time and no one at work has looked at me funny (well, at least not because of herpes!). I participate in the MSA but since the CFO does the administration I just don't submit Valtrex receipts.
I hope you have enough information so that you feel comfortable to accept this job! A new job should be a happy thing, not full of worries. Good luck! And let us know if you take the job!