The simplest answer is NO only Project Professional 2010 can connect to Project Server 2010.
Microsoft provides what is called “Backward Compatibility Mode (BCM). However BCM which allows a user to connect to Project Server 2010 using Microsoft Office Project Professional 2007 and ONLY this version can ONLY be implemented when an organization upgrades their Project Server 2007 database to Project Server 2010 format.
In the case of BeMo therefore BCM is not supported with My BeMo. In the case of My BeMo VM and My BeMo Pro, the organization would have to already have Project Server 2007 running and be able and willing to upgrade it to Project Server 2010.
Last Point about BCM: When an organization is operating in BCM some of the new features in Project Professional 2010 are totally disabled for all users. For example: manually scheduled