My opinion is that unless the scope fo the agreement is in flux, the draft contract should be provided with the Invitation for Bids, Request for Proposals or other for bid or quotation documents. The reason for that is two-fold. First, half of negotiation is setting expectations of what you need and want. The specifications or statement of work set the expectations of what you need. The contract sets expectations for how you want that to be performed and the standards you expect it to be performed to.
The second reason is the contract document sets the baseline from the perspective of price. If the supplier provided no exceptions or no assumptions with their bid or proposal, the price should be based upon you getting your contract terms. If you don’t set those expectations and standards in advance, the supplier will argue that to give you what you want in the contract it will cost you more as their price wasn’t based upon those requirements. By including the contract terms with those standards in the contract and advance, if the supplier wants to provide you less that what’s in the draft contract, you should demand to pay less as the price quoted should have been based on the contract.
Another advantage of providing the contract as part of the bid or proposal documents is if the supplier will have major problems in giving you what you want, you will know that in advance. You can help them avoid wasting their time and money preparing a bid for a contract they won’t ever agree to. On the Buyer’s side it also gives you more to consider than price alone as you can see not just the price differences between the suppliers but also the potential cost and risk differences in the terms they want changed or the assumptions or exceptions they make. If there is going to be a significant problem with getting you what you need, it's best to know that up front so you don’t waste time heading down the path with one supplier where the contract terms will be a problem. If there are non-negotiable terms you have that the Supplier doesn’t want to accept, you can focus on those right away and let them know that if you can’t get over those hurdles, there is no sense in wasting time negotiating anything else.
If I was a supplier I would also be leery of a customer that wanted to delay my seeing the proposed contract. The customer could be using that delay to get the supplier so committed to performing the work. When that happens you have two options.One is you can walk away and lose what you have invested. The other is you can stay and try to negotiate from a potential position of having less leverage. Neither of these options are good.