Yeah, entirely down to the seller. However if they've purposely selected 'or best offer', they must have already conceded they'll let it go for less that the BIN price. As mentioned, if you go to low, you may get an instant rejected as you didn't meet the sellers minimum threshold. More often than not, a best offer will be countered and you then go in for a good old haggle: "£200? I'll give ya £150, nah I'll let it go for £180, oooh, how about £170 then... " In each instance the buyer and seller has 48 hours to accept the offer/counteroffer. From a sellers POV, it'll really depend just how low ball your offer is, how many are watching the item, how many offers they've had already and how low they were. Ebay will tell you about other offers on the listing, just not their amounts.
In all instances, it's definitely worth a shot, worst they can do is say no, too low.