Using static home page and wordpress only as a blog

Would using static home page and wordpress only as a blog increase page speed instead of using a WordPress template to run the whole show?

If it did, it would only increase the speed of the homepage.

Would I achieve the same effect using cache tools?

As a general rule yes – all cached pages (unless a user is logged in, when pages aren’t normally cached) would typically be served by your cache plugin (or an advanced tool like Varnish) as if they were a static HTML file.

It’s not just about the server speed, you can make a lot of difference by optimising your image sizes, reducing the number of HTTP requests, writing more efficiently javascript or CSS and so on.

Further reading: http://codex.wordpress.org/WordPress_Optimization