Hello,

Yes,

<Can this engine run without the mechanical pump sucking and fuel pulled by injection pump?>

You deduced the solution and you would be correct.

Many diesels over the years in automotive had no fuel pump at all...only the injection pump...ie, an example would be the venerable or deplorable VW Rabbits, Jetta's etc.

Not that I am saying 100% it will be ok...only answering your question.

So, you now see, as long the the vacuum siphon effect is not lost/broken...you are good to go.

You just picked a bad time to prove it...:)

Hope this Helps,

CF