Does having the Darkness or Deep Shadows BFC in play nullify the utility of Extended Range - that is to say, make it impossible for ER to extend a figure's range beyond 6?

I believe that is the case, yes.

Originally, I would have said you can't - but upon looking at the cards:

Darkness: "Characters with a range value greater then 6 have a range value of 6 instead. Perplex may not be used to increase a range value to a number greater than 6. Powers and abilities that affect characters up to 10 squares away instead affect characters only up to 6 squares away."

It would seem only the use of Perplex to increase the range is prohibited.

So even ICwO would be able to increase it. I think this is supported by the Pulse-Wave FAQ that states:

"If a character uses a Pulse Wave in an attack the range used is half of the character’s range. When Darkness or Deep Shadows is in play, the character’s range is no more than 6. Therefore, a character with a range value greater than 6 has a 6 range when Darkness or Deep Shadows is in play. The Pulse Wave range would be half of that, or 3."

This basically says the range is halved before the attack is made. If that's the case then all figures have a 6 or less when doing nothing, rather than range becoming 6 when an attack is declared.

All that being said, I could see it being ruled via 'intent' which would prevent any modifications being made to usurp the 6 range.

So to answer your question - for me I'd rule you could do it but I'd expect the official ruling to be "no" if / when its made.

hah, looks like you found a loophole man. rep for that. there's nothing in the errata to prohibit it. i'm sure if the higher ups catch wind, they'll fix it.