Well, if things played out this way, the Earth's safety would probably come down to Piccolo having the chance to fuse with Kami and a very, very lucky epic spirit bomb, as a sufficiently strong one is going to devastate its target no matter who's throwing it. It would've been rough even with a healthy Goku around, although I suppose there is the special chamber at Kami's place. This is DBZ so we can definitely assume that everybody trains as much as possible. But yeah, no SSJ level anyway unless #17 or #18 kill a bunch of friends first.
Android #16 would've been a very interesting wild card, though. For all we know he could've turned out like #8 in the end. Also tricky is Cell's fate in this scenario, considering how much he owes his fate to Trunks (he needed his time machine) and Vegeta's idiocy. Neither would be around since Vegeta would've been either killed on Earth (a living Piccolo definitely wouldn't have let him leave) or owned on Namek.