Is it possible to safely incorporate this script without causing any
blocking or javascript errors that could hinder the functioning of other scripts in my application?
Indeed, you can
A 404 error does not impede the execution of javascript in any way; only actual errors do.
As long as the server responds with a 404 status and doesn't hang, the failure to load the script will not cause any significant delay.
This can be verified by testing different browsers and logging the time taken to check a 404 or broken link.
The fact that the browser logs the time demonstrates that such scripts do not interrupt the execution of javascript. The thread always moves on to the next script tag unless an error occurs in a script. If the URL is not found, no browser will raise an error; rather, it continues once the URL remains unresolved.
<script>console.time('Test');</script>
<script type="text/javascript" src="http://www.broken.url/file.js"></script>
<script>console.timeEnd('Test');</script>
FIDDLE
Testing in IE, Chrome, Firefox, and Opera reveals that all browsers require less than 0.0002 seconds to resolve a broken link. The duration to resolve a 404 varies depending on how swiftly the server responds, but for Google's servers, it consistently takes less than 0.2 seconds across all browsers before returning the 404 status code, enabling the browser to continue executing subsequent scripts.
Even including up to 20 scripts that all return a 404 generally consumes less than half a second for the server to handle and progress.
FIDDLE
In simple terms, you can confidently insert any script that includes a broken link or returns a 404 without negative consequences or browser hangs. Modern browsers typically take just a few milliseconds to realize that a script cannot be loaded and proceed forward.
However, avoid incorporating scripts that actually load but contain fatal errors, as they will halt the entire thread and prevent the execution of subsequent scripts.