HG makes it clear you need 3 things to jump safely:
1) two turns power in the capacitors
2) sufficient refined fuel
3) a working jump drive
It implies a 4th:
4) a working power plant with a rating no less than that of the jump drive.
So, treating it as an exigesis problem...
We note that in HG, the MD and the JD both require Power from the PP but don't use energy points explicitly; if one presumes agility is the actual performance of the drive, then yes, MD do so.
HG doesn't discuss JD power requirements in jump, only to enter jump. CT canon itself never discusses what happens in the case of a PP failure in jump, nor damage to the JD while in jump.
There is a ship which can jump on power alone - the Annic Nova. It is, however, not a HG design, nor a Bk2 design, and cannot be built within the rules.
Filling the capacitors with the PP over 3+ turns isn't sufficient to jump safely.
The net implications:
The jump initiation takes 2%Hull*JDRating EP and those must be available in a 40 minute window.
Jump drives need 1%Hull*rating while in jump.
Jump fuel isn't fused for power per se - it may be fused for plasma jets used in the initiation process, or some other use, but it isn't for power. Otherwise, the fuel could be replaced with additional capacitors.
I'll note also: other editions (MT, TNE, T4) have different assumptions, in more detail, and more information, which upon looking at it thus, doesn't match.