The problem is the biowaste coming out of the rock.
With no skimmer it's going to be a stinky situation with a crash in the bucket.
Oxygen will go so low, that you will create a toxic environment.
Wouldn't do it without skimmer.
Remember my built, where I had to place the skimmer into the display to run and keep everything aerated when the bacteria bloom started ;-)
I used the BRS dry rock for that 300 restart. But also had the Nitrate reactor full of mulm!
One thing you need to be aware on a fresh quick start is the Microfauna.
Only bacteria won't help you on the long run to keep nutrients down and the biology alive.
You need to introduce Microfauna.
Means all the thousands of critters you usually seed with a few pieces of Liverock or dirty mulm from another matured tank system.
I guess you have that covered by using your existing rock.
Recently I had someone who failed to start the tank and when I checked under the microscope the sample of the sand, there was nothing in there, totally dead except bacteria.
This tank was started with dead rock from scratch and with no live rock or any seeding. Nitrate and Po4 spiked up pretty high after 6 months, only liquid bacteria had to be constantly dosed to consume some of the nutrients. After seeding the tank, the biology became self sustaining with lowering nutrients.
https://en.wikipedia.org/wiki/Microfauna
Check these Videos I did a while ago, very interesting,
and remember this next time, you siphon water with your mouth, lol!