If the zero down offer is the only offer, and it doesn't look like another offer is coming in the near future, the seller will likely accept it, but be cautious regarding their subsequent home purchase. The seller may ask for a longer post occupancy, so that they don't pack and move out until they are postiive the sale is going to close.
The term "easily accepted" might be a stretch, but they are accepted in Seattle and as it has been stated below, a well written offer is key.
Usually with a zero down loan the buyer doesn't have a bundle of cash to throw down as earnest money, but this is one area where a buyer can show the seller they are sincere in making this purchase, thus the term "earnest" money. The earnest money can be used toward closing costs (usually 2-3% of the sales price) or, if you ask for the seller to pay your closing costs at the close of escrow, this earnest money deposit can be returned to you.
Other ways of making your offer strong are by keeping a short inspection contingency (you might want to schedule the inspection even before submitting your offer so you can demonstrate your sincerity to get the job done), short financing contingency, and a strong Certificate or Letter of Approval from a reputable lender.
Best of luck!