Yes, Multisim 10 (and higher) exposes an automation API. If you are in LV just drop the Automation Open VI and when selecting the ActiveX class search for NI Circuit Design Suite Multisim... you will see two objects MultisimApp (controls the application) and MultisimCircuit (controls circuit operation).
If you know how to control ActiveX objects from LV then you will quickly see what methods and properties are available. The Multisim Automation API is intended for controlling simulation from outside Multisim (and send and receive data) and it is not intended to control the application itself like a Excel API would do for instance. Multisim will always run hidden in the background as a process, you will never see the application.
For the following update we are increasing (a lot) the number of methods and properties that you could control from LV (and CVI, TS, VC++, VB, etc.), just wait a couple of weeks and with the new update the documentation will include a good explanation of the API, the first that we exposed (v10) is basic and functional but we were in the process of making a more useful one.
So, as far as controlling Multisim from LV there's your answer. As far as passing data from Multisim to LV without saving a LVM file you could potentially do it using the API (only for a Transient analysis) or via a LV Instrument used inside the Multisim schematic. You would use the LV Instrument to perhaps open a Shared Variable or TCP, UDP or some sort of communication protocol to pass the data to another LV app. But this is an entirely user-customized program to be made.
You would really need to learn how to automate applications from within LV first. There are some examples in LV if you use the Example Finder, and tutorials on the web that you can search for... just search for ActiveX in the ni.com search box. Is not a trivial subject to discuss in a forum but rather programming concepts that you will need to train yourself in before attempting to automate Multisim.
The LV help should be your first stop. In the web you can start here.