Is it practical to fly IFR into Hawthorne Airport (KHHR) in IMC?
Without pulling up the SOP/LoAs between HHR and LAX and SoCal Tracon, or working at those facilities to see if there's a better option, and just looking at the positions of the airports and their approaches, I'd say for an actual approach into HHR, you'd have to be vectored into the LAX arrival stream and sequenced like that.

From the approach plates, at the HHR Final approach fix you might have enough separation from LAX's 25L/R, vertically, but once you get to the end of the runway there isn't enough separation between the procedures.

Now if HHR tower can see the LAX traffic and apply visual separation that can change things as well, such that they are making sure you don't get too close, to the other final, as long as wake turbulence isn't involved.

Beyond the theoretical, just call the tower or SoCal Tracon and ask, or schedule a visit and ask.