I have the Q220 which is size below yours and yes, despite all the brushing and burning, theres always a lot of gunk hanging down under the grates....as long as the top of the grates where your food will be going is clean as possible after a good hot pre-heat and a brushing down before cooking, you will be ok.
Every now & then, like all good Grill maintenance,take off the grills, turn them upside down and use a good oven cleaner or degreaser, leave it on for at least 30 minutes or so....and I usually give it a good blast with my high pressure water cleaner like a Gerni or K'Archer, let it dry in the sun for a bit then give it a good oil over.
Sometimes If I leave it too long between clean-ups...i gotta use a flat sided screwdriver to scrap off some grease on the underside (heck if I know how it gets in under there..hasn't grease heard of gravity)That's all I do and been using my Q's 5 days per week for nearly 5 years.It's a cooking device...it's gunna get greasy so take it apart and give it a good clean up every 3 months...all I can advise.
Cheers
Davo