Yes, make sure you have your account activated with your supplier. Once you make a sale, you then process that order with your supplier and they will ship direct to your customer.
It doesn't matter what products you list in regards to your supplier, however make sure you do your research to make sure the items you are listing are competitively priced at the very least. You also have to make sure you have done your caculations correctly, allowed for any fees, such has listing fees, selling fees, payment processing fees and shipping fees, when pricing your items.
This is an area where many make mistakes, miscalculating their fees and getting burnt at the sale end. So when you're checking your cost competitiveness, make sure you are basing that on a total transaction calculation.
BTW, you're not limited to just using one supplier either, so you can list products from multiple suppliers if you feel you find other products you want to see that one supplier doesn't have. That is one of the benifits of dropshipping, the flexibility of building a large stock profile at no to low expense. Just watch out for listing fees, because they can still hurt you if you start listing heavy without a good sell through rale to cover.