Consequences of including an external script file in a GTM tag

How is this file loaded?

Asyncronously, keeping script order.
Despite you writing it as an html <script> tag, GTM loads it creating a DOM script element instead.
This is roughly the code used (not taken from GTM directly as minified):

var script = document.createElement('script');
script.src = '/path/to/file.js';
script.async = false;

Does it affect the loading time of the page?

Yes. While the way GTM loads scripts impacts page loading speed as little as possible, scripts still have a significant impact.
There are ways to mitigate the impact, although third parties are generally harder to optimise.

In you GTM custom HTML tag, you can even use the async or defer attributes:

<script async type="text/javascript" src="/path/to/file.js"></script>

Further reading: http://davidwalsh.name/html5-async

And if you are using HTML5, type defaults to text/javascript, so you can leave it off.

Alternatively you could load asynchronously using an anonymous self invoking function:

<script>
(function(d,s){
var e = d.createElement(s),
m = d.getElementsByTagName(s)[0];
e.async = 1;
e.src = '//externalsite.com/file.js';
m.parentNode.insertBefore(e,m);
})(document,'script');
</script>