Not unless you want to use the LED for supplemental lightning. LED's don't draw but about 20 ma sometimes less so it would be less of a load than a Blinky. You could make a small circuit fo monitor the battery and use an led to give a visual indication that you need to charge or change the battery. something like this would be easy.
http://www.edn.com/ednmag/archives/1...1395/08di4.htm
I started thinking about the voltage difference and I don't think it would be a big enough deal to even need a regulator using a single cell. If you have ever used the the Energizer Li batteries (the silver ones) they measure about 1.9V per cell brand new. I used to use them in my camera that uses 4 AA batteries and didn't have an issue. I never checked them when I started using them and it wasn't until I was going through a pile of batteries sorting them into good and bad piles that I discovered they were that high. I also used them in my older Kodak that used 2AA's. At 4.2V right off the charger for the 3.7V cells you are only dealing with a .4V difference. If it would make you feel more comfortable you could discharge your battery to 3.8V on your charger.
Jeff