While it can be installed heres a couple articles...
http://articles.timesofindia.indiatimes.com/2013-10-01/computing/42573959_1_iphone-4-users-ios-android-phones
http://www.phonesreview.co.uk/2013/10/01/ios-7-battery-problems-reported-for-iphone-4-and-4s/
So perhaps those are worth taking a look at before you actually update the iPhone 4 to see if you really want all that stuff.
Note: I also updated main post with a preview...