Lets hope his Son is not good enough for NBA, so an NBL team can throw him a lifeline, so LeBron comes as well when he retires from NBA.
Seriously though, if his son turns out to be good enough, no reason they couldn't be together. Most champions like LeBron prefer to go out whilst still on top. But this might give him incentive to stick around for a season or two, even if he had to take a pay cut and warm the bench.
Would a team go for this? Fuck yeah. The Marketing alone would be a goldmine.
To get back to the OP's question, I suppose the question is how much extra value it would add to Junior.
Let's say, hypothetically, Senior is a FA and on the brink of retirement when Junior becomes eligible, and lets it be known that he will sign (for minimal coin) to whatever team drafts his son. Would that push his son a slot or two up the draft??
I reckon it might, depending on how desperate the team is for marketing opportunities.
Off the top of my head, I'd imagine it might elevate him from just outside contention into a draft spot. But as somebody said above, I don't feel that a team would use a valuable pick, unless Junior warranted it. As was said, you don't jeopardise the future of the franchise for a photo-op.
I guess the other issue, is whether the NBA has rules that would view this as draft tampering?
The big personal question for the family though, is do you really want to stick Junior with that label? "Only got drafted cos of his Dad?" Dad's can certainly open the right doors, but there;s a big difference between getting your kid a try-out, and actually directly influencing his draft.