If there's no reserves, I assume the Incubator sector (or whatever sector is consuming the most juice) would just stall out and stop producing anything, and/or enter a "battery-saver" mode where it, like, consumes half juice in exchange for half core production. I can't imagine it'd be too hard to keep your juice production and consumption balanced, so the negative side would be more of a fail-safe, and wouldn't have to be that smooth, gameplay-wise.
Either that, or it'd stop you from buying any upgrades unless you had enough juice production to sustain them. A warning popup would probably be good either way, assuming you do go with juice-per-minute. Having the total in and out in the milking sector makes a lot of sense, yeah. Although each transformation should probably say how much it increases consumption by.
Yeah, if you didn't have the support team literally milking the milkers, that'd be a massive missed opportunity.