No. He'd probably hurt Johnson more than Fury did and be more aggressive, but if Johnson can hang in for 12 rounds with Vitali he can hang in with Price. The other big difference is that Fury approached the fight differently than he would have in the past - he was trying to put in a more disciplined performance, and get out of some of his previous 'bad' habits. Price doesn't have those habits to shake off, so his biggest struggle would be going the whole 12 rounds for the first time. I could see Johnson stealing a few of the middle rounds if Price tired, but I reckon Price would win by points and pick up most of the rounds.
Johnson was a big step up for Fury, and a good measuring stick for him when you look at the level of opposition he's fought. For Price it'd be a big step up too - it's not going to be as easy as putting away the likes of Sexton, Harrison and Skelton. Johnson knows how to go into survival mode against a big hitter.