Software piracy is a problem, but its not your problem.
You've raised your concerns with your employer, and they have stated that they may have licences, but haven't kept track of it. As other posters have stated, its important that you raise the liability issue with your employer, but unless your responsibilities at the company include licencing compliance, don't press the issue.
Because they may be correct that they do have enough licences, in which case blowing the whistle will bring unnecessary auditing on the company and if they take a hit from it, they will look for the person who blew the whistle and if you've pressed them about the matter they'll pretty easily figure out it was you.
If you are seriously concerned about the matter, get their response in writing - email the IT department and ask clearly and concisely that you need a Windows licence. If they reply with a licence, great.
If they don't provide you with a licence, print a copy of the email, make sure you keep an electronic copy, and go on with your life. Make sure you have a clear paper trail that shows your diligence and you are in the clear.
Update based on comments:
In the comments people have mentioned the level of responsibility of an employee regarding ethical matters. Obviously with ethical dilemmas there is a sliding scale to how responsible you are to your company, the aggrieved party (in this case software vendors) and society at large.
If you can demonstrate due diligence by properly raising this within your company, it is very unlikely that a group like the BSA would consider you at fault. Considering the BSA has come under criticism in the past for their heavy-handedness if you can show that you raised your concerns internally they would consider you having done your duty.
This is especially true if your role within the company isn't an IT role, or one that explicitly covers software licencing.