Although each bank is different, my experience has been that they will reveiw the BPO vs the price of the contract and then make any recomendations before submitting for approval. This could mean that they ask for more money, or that they think it is a fair offer. Their job is to get everything in order to submit to the investor for approval - if the BPO came in higher or outside of an acceptable % required by the investor, then they will counter before submitting for approval. Some negotiators receive compensation based on how small those percentages are (had a case with Wells Fargo where they tried to get an extra $65k out of the buyer so that the negotiator could make a bonus!) but most are working off of parameters set by the investor. These could be maximum closing costs allowed, agent compensation, sales price vs. market value, etc. The investor is the one who has to sign off on the package - the negotiator just cuts out all the paperwork to put it in perspective for the investor.
As far as timelines go, it's first in first out so it just matters when the individual gets to it!