As far as I can see, no. Especially since the Super Saiyan 4 transformations are being treated as bonuses now. None of the recent DBZ games as far as I remember have treated GT as canon, which is understandable since the inclusion of the Super Saiyan God form and Goku's dramatic boost in power (as he pretty much kept his God power) kinda contradicts his level of strength in GT.
How "dramatic" the boost he got from SSJG in comparison to the power in GT is not all that concrete, all we have is goku SSJG able to fight Beerus toe to toe who himself only has a notable feat of pwning a SSJ3 with his finger, something that could easily be done by the likes of SSJ4 Goku,Omega Shenron, and SSJ4 Gogeta by example.
And lets not forget him pwning Frieza and cell in base form during the events of GT which shows his power was immense in comparison to his power in DBZ before the events of BOG.
But for the most part I agree with the rest of your post, but we did get a scan of SSJ4 Goku fighting Super 17 in what looks like the exact same area he fought him in GT so the chances of a storyline mode of the events of GT is possible.