I'm going with maybe, but for reasons not previously mentioned.
Let's talk about star drives and their power output, then compare that to the power output of an explosion.
Your ship is capable of travering deep space casually and easily, it's not a generation ship or you wouldn't be exploring event horizons up close, hence it has a superluminal drive system, the power output of which is quite simply magnificent.
In short, an explosion can't match this. Not an Orion drive, probably not even a supernova.
they are precisely on the "Drama Line", the altitude at which it is possible to blasted to safety by a makeshift bomb cobbled together from bits of your ship that really shouldn't be going bang. Below the drama line, all you'll be able to do is to send out a tearful goodbye message, possibly telling your children how proud you are of them, before you plummet to your doom and/or explode. Above the drama line you can just fly away, and as such no-one is really interested in that flight regime. - Starfish Prime in the comments
There are several Drama Lines to define, importantly the explosion Drama Line is considerably further out than the star drive's Drama Line.
The quirk of black holes is that you need to be able to travel faster than the speed of light to escape the event horizon. Your star drive can already do this.
Now you need to tell a story
The important part is that you're still outside, but approaching, the explosion Drama Line, which leaves you well outside your star drive Drama Line. Something has gone wrong with your star drive, technology is now a character in your story, you can begin the technobabble.
You get a choice, and you can build up to it. Either you blow up the drive now and escape on the explosion Drama Line, or you try to hold out and fix the drive and get out ahead of the star drive Drama Line. This inverts the traditional plot where the drive repairs fail and then you blow everything up.