Absolutely no reason why you can't do both, however I would be concerned about any company that just offered you a wholesale opportunity without knowing anything about you, even offering you a representatives position with no CV has a strange smell about it to me.
It shows that they are not particular about protecting their brand, and that is usually the first thing a brand owner wants to protect because that is where the value of their product is maintained.
I'm not saying that you wouldn't do the right thing by their brand of course, but for them to simply be offering wholesale opportunities without any checking at all reeks of pure desperation on their behalf.
Sounds to me like they are looking for an injection of cash, and that would come from you buying in your stock to wholesale. So yes, you would require stock and space to be a wholesaler, however you may be able to sell from just a few samples that you would use at the time of the pitch, and then ship direct from their warehouse to the customer.
Honestly, you really do need to take a good long look at what this company is all about, and just what it is they are offering you before you make any real commitments to them in my opinion.
Opportunities do exist, but so do scams!
If you do decide to go ahead with some form of involvement, I would suggest buying in a few samples and getting your feet wet by visiting a few buyers and seeing how the products are received. That will give you a good baseline to work off.