Probably, but it's hard to gauge just by how much. I think the number is miniscule and it's nice not to get locked with 3-4GB in the future as I'm not planning on selling 1xxx series cards in less than well over a year.

I could only find estimates on memory power consumption which vary wildly:

http://www.anandtech.com/show/10193/micron-begins-to-sample-gddr5x-memory (1/3 of the page)

Based on other sources older cards consumed 4.35 W per gigabyte of GDDR5 (17.4W for 4GB and 34.8W for 8GB) but the same source says it's closer to 20W or slightly more for 8GB.

There are also much higher numbers, like 50W for an R9 290X.