I just tested this on my test site. With "Search Profile" unchecked it disables the member search feature, and gives the user a limited permission message on the search page, but the member can still browse the members list, and with "View Profiles" still checked, they can view the profile, and contact the user from their profile page. If "View Profile" is unchecked, they can't view the profile, and therefore can't contact the user. If you still have it set where they can initiate a chat dialog, I would guess they can still click on the "chat now", if the member is online, and contact them that way.
If you want to let them view profiles, but not initiate contact, and not allow them to use the search feature. This should let them browse members, but not initiate contact. The user can select who sees their profile newsfeed in their privacy settings. This can help keep contact from occurring through their profile newsfeed.
1. disable start chat dialog.
2. disable start mail dialog.
3. disable search users.

thanks, any kind of downside to that?

Really depends on what you want to achieve.  deselecting the "search users" will only remove the ability to use the search. As stated above; they can still browse the members page, and visit profiles. They just won't be able to use the advanced search feature. How much you won't to limit basic users is up to you, and the limits of the platform. Personally; I would have a few things that may want to get them to upgrade a membership, and being able to do more than viewing a profile can be one of those.