The question found here is similar to mine:
Can I leave the batteries in my camera?
Some users alluded to the answer to my question. However, I am specifically asking if any battery energy at all is used while my Canon 5D Mark ii is off and the battery is still in it. I'm talking about leaving the battery in the camera for (eg) 2 weeks.
In other words, will the battery have any more juice (even a small amount), if it is stored outside of the camera?
First, we need to understand that your battery will lose some of its charge even when stored outside of your camera. This is what is referred to as "self discharge" or "shelf life." Rechargeable batteries tend to self-discharge at faster rates than their non-rechargeable alkaline counterparts. Historically, rechargeable Lithium Ion (Li-ion) batteries are better in this respect than Nickel-Metal Hydride (NiMH) batteries, which are better than Nickel-Cadmium (NiCad) batteries. Newer Low Self-Discharge Nickel–Metal Hydride (LSD NiMH) batteries have improved to the point that their self-discharge rate is similar to Li-ion batteries. The rechargeable LP-E6 battery you use in your 5D Mark II is a Li-ion battery.
Self discharge is one reason why it is recommended to recharge your batteries a short time before you plan to use them again, rather than immediately after using them if you know you are going to store them for a while.
Will the battery have any more juice (even a small amount), if it is stored outside of the camera?
Very, very minimally, yes. Since the battery will lose more of its energy due to self discharge, the difference between leaving it in the camera and outside the camera would probably not even be measurable unless you have some very sophisticated equipment.
But if you remove the battery every time you store the camera you might be exchanging one issue that you consider very minor for another that you might not consider to be as inconsequential.
The Canon EOS 5D Mark II uses very little energy when it is turned off. It does use a very miniscule amount to maintain the date and time internally. When an LP-E6 battery is not supplying the current for that purpose, such as when you change LP-E6 batteries, the camera draws power from a CR1616 Lithium button cell to maintain the time and date. Leaving the camera without an LP-E6 battery installed for extended periods of time will cause the CR1616 backup battery to deplete more quickly. This won't happen overnight. When the camera is stored without an LP-E6 battery, if the CR1616 is fresh it will still maintain the date and time for several years. The CR1616 should last even longer, though, if a charged LP-E6 battery is usually kept in the camera.
I've owned my 5D Mark II for six years. The original CR1616 battery that was inside the camera when I bought it new is still maintaining the date and time when I change batteries or leave the camera with no battery for a few hours or even days. But most of the time I've owned the camera it has had an LP-E6 inserted. Since a 5D Mark III has replaced it as my primary camera body there are times when I might not use it for a month or two with an LP-E6 battery inside. When I pick it up to use it again the battery has about the same amount of charge left as it did when I previously used it.
Do note that some of the more recent models from Canon, particularly those with built-in WiFi and GPS, tend to deplete installed batteries at a much higher rate when turned off. They do so even if the WiFi, GPS, and (in the case of the 5D Mark IV) touchscreen are disabled. The Canon 5D Mark IV, 1D X Mark II, and 7D Mark II have been notable in this respect. These newer models don't have a time/date backup battery either. Instead they contain capacitors that are charged by the Li-ion rechargeable battery when it is installed in the camera. The energy stored in the capacitors is then used to maintain time and date when there is no Li-ion in the camera. I typically store my 7D Mark II with no battery installed. I have yet to experience a case where the camera loses track of the date/time, but then I rarely go much more than a week at a time without using it.
Two weeks? You have absolutely nothing to worry about.
The only time this is a concern with Canon DSLRs is if they have GPS and it is left on. If your model does have GPS, even with the camera off the battery will be depleted quite quickly. Since the 5D mk II doesn't have GPS - you can easily leave the battery in it for weeks without any additional battery drain beyond normal self discharging.
