Yes the controller will still work with a parallel glow plug arrangement.

Just make sure you delete the "bed springs" between the plugs, these are resistor wires, and put regular wire between the plug terminals.

And be sure to delete the grounded wire at the end of the line!

You will end up with the "hot" wire coming from the controller hitting the terminal on the rearmost plug (either #4 or #5 depending on your engine), then you want to make jumpers to each plug in succession to the front of the engine.
Plug #1 at the front of the engine should only have one wire, the jumper from #2.

On your series plugs, you have stacked terminals (there is a spacer between the two connections on each plug). Now since you're making a parallel circuit, the two wires at #2 through the last plugs can (and should) touch each other on the terminal.

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The OM 642/722.9 powered family
Still going strong
2014 ML350 Bluetec (wife's DD)
2013 E350 Bluetec (my DD)

both my kids cars went to junkyard in 2023
2008 ML320 CDI (Older son’s DD) fatal transmission failure, water soaked/fried rear SAM, numerous other issues, just too far gone to save (165k miles)
2008 E320 Bluetec (Younger son's DD) injector failed open and diluted oil with diesel, spun main bearings (240k miles)

1998 E300DT sold to TimFreeh
1987 300TD sold to vstech