Indeed, the more tables you get, the bigger the project will become and it will become slower to load. The more relations you'll have is a bigger factor though. thousands and thousands of relations inside a project might slow it down more than a thousand tables.
Also, if you have thousands of stored procedures in a project, it will become slower to load, so keep these to a minimum. There's no maximum of tables you can have, it's that thousand or more tables and multiple thousand relations will make the load/save process a tad slow. The designer itself doesn't become slower (well, perhaps the reverse engineering of entities of course will become slower as well). the one downside of the system is that if you have many relations between the same entities (so A and B have many relations) it might cause a lot of m:n relations to be generated which could slow the system.
As thousands of entities will result in a large generated code base, you want to compile that on the command line as vs.net is slower to compile that than a command line compile action.
What's the number of tables you're looking at exactly?