First of all, it is extremely rare that the theme parks halt admission because of capacity issues. You can read more about park capacity issues
HERE and
HERE.
If one of the Disney parks does reach capacity, there is no general loudspeaker announcement or anything like that. However, all the bus drivers and many other cast members will be informed and the information tends to spread rapidly throughout the parks. If a park if full to capacity, you will likely hear about it within the hour.
When traveling with a group that may split up while touring, even within the same park, I would STRONGLY suggest that you have a cellphone or walkie-talkie available so that you can easily communicate during the day. I can't tell you the number of times I've told my husband something like, "I'll meet you by the exit to ride X." And even though we both know every inch of Disney World, we end up waiting in different spots. Similarly, rides do occasionally have a temporary pause, restaurants do occasionally run late, and guests do occasionally end up in the first aid station. With a cell phone handy we can easily communicate and resolve these issues that might cause a meeting mishap. Without a cell phone, everyone is frustrated and confused.
If you're meeting the rest of your party at another park, just give them a call before you head over to make sure everything is OK. Then you're all set to meet up and have a great time touring together.