That's going to be one of those situations that are better served for later drafts.
Yes, if one player wins the job outright they will see a considerable jump in ADP as the season draws closer. There's really nothing you can do about it right now other than take them where their current ADP is and hope you get the right guy or avoid the situation altogether. If you pick correctly, then you'll probably be handsomely rewarded. If you miss, then you've probably wasted a pick unless an injury occurs.
There's a lot of risk involved in fantasy football, and this would be one of them.
Now on the other hand, if they become a RBBC, they might not even be worth the 5th round pick you need to use on them now!