Replacing the mixture control with a pre-charger

A couple of days ago, I downloaded a Diamond HK36 motor glider for Flight
Simulator. Upon closer inspection of it, I found out that it has no mixture
control lever, but it has a low-power turbocharger. So it got me wondering:
1.) does the real aircraft have that and 2.) can it be possible that, since
a motor glider is not required to climb very high, this system would be
installed to make operations simpler? It would make sense, since the charger
would supply the engine with near-sea-level air density up to the altitude
from which it could begin the glide, so mixture control would be
unnecessary. If this does exist on real-world aircraft, what are the
advantages and disadvantages of that system? And does this system simplify
or aid in any way in starting the engine in-flight?

Triple Delta