Of course it's possible, you'll just want to write a function that finds the middle of the content then ads your block. Something like this
//get the content
$content= get_the_content(); //get the content as a variable
// find the middle
$halfway_mark = ($content_length/ 2);
// clip off the first half
$firsthalf = SUBSTR($content, 0, $halfway_mark);
// find the last '<br>' in the first half
$end_mark = STRRPOS($firsthalf, '<br>');
// add in the adblob at the position found above
return SUBSTR($content, 0, $end_mark) . "<p> YOUR AD HERE p>" . SUBSTR($content, $end_mark);
This is totally untested and may need to be reworked I got the code to find the middle from here.
Edit: As OneTrickPoney pointed out we need to check for HTML tags one method may be to use php's strip_tags() function . and add something like this after the first content call:
$content = strip_tags($content) //remove html tags
the problem will be adding the tags back at the end.