Will Lockheed Martin Flight Services send me ACAS, EasyActivate™, and other text messages if I file my flight plan through ForeFlight Mobile?
Based on my personal experience, the answer is NO (as of the time of writing). I use both systems regularly, and have discovered the two do not share flight plans at the user account level. ForeFlight uses its own account (and not individual user accounts) to interact with Lockheed Martin Flight Services. Because of this, it appears that LMFS has no way of knowing which user account is associated with a flight plan filed through ForeFlight.  

Identifying data within the flight plan itself (i.e., name and phone) are not processed by the filing system, merely stored for later retrieval if needed. I mention this because LMFS can (upon request) associate tail numbers with a phone number, so that when you call them on 800-WX-BRIEF your profile comes up on their screen automatically (though I have found this to be less useful than one might think). 

In order to use the services you have identified, you will need to file your flight plan directly on the LMFS web site (and have your notification settings configured properly).

With that said, all of these functions (with the exception SE-SAR), have been available directly within ForeFlight for some time:

ACAS/ATC notices - if configured by the user, sent via push notification (http://blog.foreflight.com/2014/11/24/6-5-brings-flight-notifications-and-notam-advisor/)

EasyActivate/EasyClose - flight plans can be amended/canceled/activated/closed within the File &amp; Brief window (http://blog.foreflight.com/tag/flight-plan-filing/#attachment_4045)

Close reminder - sent via push notification (https://support.foreflight.com/hc/en-us/articles/205052928-What-are-push-notifications-)

Over the past couple of years, ForeFlight has been aggressively working towards tighter integration with LMFS, so I would expect additional functionality to be forthcoming (purely speculative, since they are very tight-lipped about upcoming enhancements).

UPDATE:

It looks like LMFS now offers integrated services with a number of providers (but not ForeFlight). My guess is ForeFlight doesn't allow it because it was already offering the same services and now needs to figure out a way to ensure users don't get duplicate messages: