Yes, they will.
You will find the WordPress template heirachy useful, particularly this graphic:
This shows how the templating system works – in particular, how WordPress will select the most specific template it can find, with fallbacks to the least specific (eventually, to index.php).
In your case, you’ll see in there that single-$posttype.php falls back to single.php, then singular.php, then finally index.php (direct link to single post section of docs).