I find that pretty unlikely. The Belk Bowl is a Tier 1 bowl for the ACC. I think it very likely that UNC will grace that bowl this year as they tend to really like a NC team in it for revenue purposes. Some say they created it to ensure that UNCheat would have a place to go east of the Mississippi after a 7/8-win season.
ACC has 11 qualified bowl teams. Here's how it will likely play out. (Warning... this is not pretty.)
We have Clemson (likely CFP) and FSU/UL (likely Orange) that are pretty well set to go higher than Tier 1 (CFP/NY6).
That leaves six qualified ACC teams (FSU/UL, VPI, UNC, Miami, Pitt, and GA Tech) to vie for four Tier 1 bowls: Belk, Sun, Pinstripe, and either Taxslayer/Music City. Having lost to UNC, Miami, and Pitt, it is unlikely that we will land in one of those. VPI and UL both have to go higher than GA Tech, due to conference record. UNC is almost certainly going to be one of those chosen due to the Tobacco Road Mafia. This leaves Miami, Pitt and GA Tech to vie for that last Tier 1 spot. Say Miami gets that spot due to their following in NYC.
That leaves five teams - presumably Pitt and GA Tech from the above teams (both 8-4), plus Wake, NCSU, and BC (all 6-6) to vie for four Tier 2 bowls: Military, Independence, Quick Lane, and St. Petersburg. Due to conference record, both Pitt and GA Tech have to go before BC. Most are thinking GA Tech is heading for the Military Bowl and Pitt for either Quick Lane (due to geography) or St. Petersburg (there are far worse places to spend a few days at holiday time).
In this scenario, some ACC team is left out unless an at-large spot opens up or the B1G gets punted from the Citrus. If the Citrus Bowl decides to take an ACC team, it opens up another slot in our Tier 1/2 bowls, everyone bumps up a slot, and UNC may go to the Russell or Taxslayer (Gator) Bowl instead with Pitt or GA Tech in the Belk.
Kind of a mess right now.