That would work as the Manfrotto swivel is doing the heavy lifting. I tried something similar with my Quadra and SFII and umbrellas. The things to bear in mind are:
1) You need to find a way to ensure the lamp doesn't follow it's natural tendency to want to flop around to be underneath the shaft. The OP looks like they down it via the positions of the cord and the Quadra swivel lock knob. The lamp is VERY light but it still wants to roll over around the shaft. You could also just let it do that and leave it there.
2) You still need to be careful mounting the umbrella - straight in and slowly until everything is secure.
3) It's a slower setup. Mount light on umbrella, hold secure so doesn't flop around or you touch the tube, etc, then mount whole enchilada into Manfrotto, then pull lamp rearward and secure (from flopping over - or let flop and leave it under shaft)
4) The lamp will go no further fwd than the point where the 7mm (SFII) removable extension screws into the main shaft. At that juncture any attempt to shift the lamp fwd will crack the tube.
The ideal approach would be to cut off that asinine tube and mount the lamp directly to the top of the Manfrotto using a combination of Manfrotto/Avenger bits between the Manfrotto umbrella mount and the Quadra's own mount so that lamp is in position as shown (likely with it's swivel adapter pointing upward). This would hurt resale, BUT would allow three things:
1) Use of ANY umbrella or umbrella-based modifier as no longer constrained to 7mm dia.
2) You could 'focus' the light by shifting the whole unit fwd/backward relative to the face of umbrella, etc.
3) A quicker setup. Drop modified Quadra onto a Manfrotto swivel mount, insert SFII shaft, etc into Manfrotto and you're good to go.
I considered doing something similar but decided to pull the plug on the idea and move on. I have enough home reno and Photo DIY work on my 'to do' list already. I also didn't feel I should have to add to that list because Eli decided to glue a glorified 7mm straw on to a $20 piece of plastic (flash tube aside) and charge app. $375 (new head - flash tube) for it. Now, if I only wanted to use the Quadra with it's reflectors and it's $15, oops, um, $125 softbox, then that would be another story. For basic shoot & scoot with it's intended modifiers, it's a great kit and powerful, but beyond that some DIY work and MacGyverin' is needed.