Stars burn whether the energy they produce is used or not, so this doesn't accelerate the heat death of the universe. You'd have to merge stars for that (because larger, heavier stars have a higher rate of fusion).
Technically if you wanted to maximize energy production you would split every star apart into dwarf stars that lived 100s of billions of years. You don't want them burning at all. Then you would take their matter and dump it in a black hole and capture that energy.
Not to mention if you could get total conversion of mass to energy going, you could just scare all the stars into inert hydrogen icebergs and use the hydrogen to fuel your total conversion reactors. Much more efficient than fusion.
