So, why do you want to use a choke-input filter in the first place?
AFAIK, they are most useful in giving you better output voltage
regulation under varying load than a capacitor input filter. They have
the added advantage that you can get more DC _power_ from a given
transformer by using a choke input filter, because although the output
voltage is lower, the RMS transformer winding current is lowered even
more.

BUT--the voltage regulation advantage is lost if you try this with a
half-wave rectifier circuit, because you cannot maintain constant
enough current in the choke. To get the voltage regulation, the
current in the choke must not drop to zero at any time in the cycle,
and that's not going to happen while maintaining reasonable output
voltage in a half-wave circuit. (There's some limited help if you put
a "catch diode" to keep the voltage across the choke from swinging too
far negative, but that's not enough to get the advantage of the
full-wave circuit.)

In addition, as John says, in the circuit as drawn, the choke is simply
in series with the transformer secondary, so you must reverse the
current in it between half-cycles to get conduction on both
half-cycles. It will not behave anything even close to the way that a
full-wave rectifier feeding a choke input filter will.

Suggest you try a simple Spice (e.g. the free LTSpice from the Linear
Techonolgy website) simulation of this and the normal full-wave
circuit, and look at the huge differences. Note especially what
happens when you vary the DC load on the output.

Cheers,
Tom