Well naturally is a lowball offer is put in. We are led to believe the 2 teams were around the 25 million pound mark in the summer. It would be hard to make a serious argument that his value has really gone up to Barcelona in that time but hey ho. This to me seems a fairly sensible figure to work from and I would happen to agree with you that if either side deviated much beyond this figure it would be seen unfavourably in terms of the wider etiquette around the negotiation. So yes, if Everton bid £10 million pounds and try to pressure Gomes to sulk to get the move, I daresay it will not be met favourably by Barcelona. Likewise if Barcelona look to shift the price dramatically upwards to say £40 million then you will see a similar response from Everton and the player.
I go on the assumption that Everton are willing to pay around the figure that was outlined last summer (with a nominal potential increase upon it as a good will gesture). If this is willing to be done, the deal will be done quickly.
As you indicate, if either party try to move much beyond that point it will get messy. I have to say I hope Everton don't do this, there is a good working relationship there and it would not be a conducive way to conduct business.
However the OP I made was on the assumption that Everton and Barcelona continue to negotiate in good faith, which I see no reason not too.