filtering the_excerpt()

If you remove_filter( 'get_the_excerpt', 'wp_trim_excerpt' ) and add your own get_the_excerpt filter you can do this.

The default filter (wp_trim_excerpt()) can be found on line 2023 of /wp-includes/formatting.php if you want to just modify that. The extent of what you need to do is just modifying which tags are allowed in strip_tags().

overriding functions.php

As for overriding the functions.php, the codex is pretty clear on what you need to do.

update: Here’s a good tutorial on allowing tags in the_excerpt()