Straight to the question. Is a coin dealer likely to offer less for a gold bullion item in trade for a coin than a bullion dealer's straight buy-back? This is really not that big of a consideration but .... I have a 1 ounce bullion bar that, counting everything, has me about $40 ahead of my cost (original spot + seller's markup) PLUS his buy-back charge. [The bullion dealer's buy-back charge is $10 below current spot.] If I find an item at the upcoming Whitman show that I'd like to do a "trade + cash" for, is a coin dealer likely give me the same amount for the bullion bar?
What would the coin dealer have to be able to do to accept your deal ? He either has to be able to make a profit when he sells the bullion, or he has to be able to mark down his item enough to make up for what he doesn't make on the bullion item when he sells it, and still make a profit. Thus what Tom said is true, it depends because every situation is going to be different. While it may be somewhat more convenient for you to do an all in one deal, I have usually found it best not to. The more variables you add into any deal, the less likely you are to get the deal.
My instant reaction is YES. Coin dealer do not specialize in bullion, and bullion dealers do. Therefore, and I am generalizing, the coin dealer will want to "untie" his money from the bullion as quickly as possible, and that means, unless he already has a customer for it, selling it to the bullion dealer. Since there are opportunity cost and transportation cost to account for, the coin dealer must pay less for it than will the bullion dealer.
My thinking is that the coin dealer would value the bullion piece at spot (or slightly below) and charge his retail price for the coin I'm interested in. Therefore he'd have his profit from his listed price of the coin I'm buying with no loss from the bullion item. Mostly I think a coin dealer wouldn't do it just because of the annoyance factor (having to go to another table to cash in the bullion piece). I suspect I'd have to be a preferred customer with the dealer I approached. In my case that would limit to 2-3 dealers (maybe). I was just trying to streamline a transaction by eliminating a third party such as a bullion dealer.
And therein lies the problem in your thinking. What the dealer has to look at in regard to the bullion is what he can sell that bullion for. The person who buys the bullion from him, (in most cases that's gonna be somebody who deals in bullion), is only going to pay 10% or more, less than spot. The dealer knows this and knows he has the potential to lose money on the bullion. To avoid that potential loss he is going to offer to pay you less than what he thinks he can sell it for. Could he break even on the bullion as in your scenario ? Yeah, he could. But he knows the odds of his doing so are slight so in most cases he won't take that chance. And if he's not willing to take the chance then that means that you lose on the bullion side of the deal. The scenario you describe is no different than when you trade in a car. The dealer will tell you he is giving you $5000 for your trade. You think that's a good deal because you know your car is only worth $3000 to a dealer. But the dealer isn't giving you $5000 for your trade, in reality he's only giving you $3000 and dropping his price of the new car by $2000 so he can make the deal. If you came in without a trade, he'd still drop the price by $2000 to make the deal. Bottom line he makes the same deal every time avoiding any potential loss for himself. But if you sold your car yourself as a separate deal to an individual, you might get $3500 or even $4000 for it. A better deal for you because the new car is going to cost you the same no matter what you do.