It's unclear if the two issues are related. While the battery drain issues are just that, issues with reduced battery life. However, the VFUK warning to customers is about 3G performance. The company sent the following text message to end users:
If you've not already downloaded iOS 6.1 for your iPhone 4s, please hold off for the next version while Apple fixes 3G performance issues. ThanksIt also posted the following message on its support forums:
Some customers may occasionally experience difficulty in connecting to the network to make or receive calls or texts or to connect to the Internet. Apple is working on a solution to their software issue. These connection problems are intermittent.In terms of the battery life problems, there are multiple threads spanning page after page on the Apple Support forums, and it appears that it appears that the pace is accelerating as time goes on. The majority or replies to the threads appear to be coming staring Feb. 8.
While Apple’s investigations continue, we would recommend that anyone who has not yet installed iOS 6.1 on their iPhone 4s should delay doing so until Apple has confirmed that their problem has been fixed.
Examples of threads are here (11 pages), here (17 pages), here (six pages) and here.
That last one has a possible suggestion. One person said a hard reset fixed his issue, but while he said he would follow up with a later post confirming whether or not it continued to work, he did not.
One possible cause (among multiple possibilities) is an excessive logging issue between Apple Mail and Microsoft Exchange. The problem can apparently devices to get into a sync loop, which could obviously cause excessive battery usage.
Whether or not the VFUK warning and the battery issues are related, it's been reported that iOS 6.1.1 has entered developer testing, so be on the lookout for an update.