Yes its doable, although (IMHO) the limit at which GET becomes cumbersome is significantly greater than the threshold at which a user interface for providing this much information becomes unusable. Also, the more complex a query you submit to a conventional search engine, the more effectively it can be resolved.
But I'm guessing you have your reasons.
The simplest way, from the information you've provided, to achieve this would be to change the form method at run time from GET to POST using javascript, e.g.
<form method='GET' id='searchform' target='search.php' onsubmit='
if (document.getElementById("searchdata")) {
if ((document.getElementById("searchdata").length >$some_threshold)
&& (document.getElementById("searchform"))) {
// 2nd if in case this moved to action for button
document.getElementById("searchform").method="POST";
}
}
return true;'>
<textarea name='searchdata' id='searchdata'>
</textarea>
<input type='submit' value='go get it'>
</form>
Which also downgrades nicely for non-javascript clients.
C.