Yes, the naming convention enforced by StyleCop (which enforces the MS coding rules) is 'no underscores, camel case' for private instance fields.
It is of note that constant/static readonly fields have the 'Pascal case' naming convention (must begin with uppercase but not be screaming caps).
The other naming conventions are holdovers from C++ style, which was the initial style used to code C# in since that's where the C# team came from.
Important Note: Whether or not you use this coding style is entirely up to the development team. It's far more important that everyone on the team use the same style than that any particular style be used.
OTOH, MS chose this style after much deliberation, so I use it as a tiebreaker. If there's no particular reason to go one way or another with a coding style, I go the way StyleCop goes.