If we all HODL, it can actually go either way. But most likely the price will increase since there will be no people selling for others who wants to buy. So basically, as long as the demand is there, buyers will increase their offer so that HODLers will most likely sell their coins. If there is no demand, then there is no point in selling since no one is buying.
This isn't true, there's no way to go both ways if EVERYONE (and yes, we're talking about everyone here) is HODLing. If no one is selling, or just for the reasons of this theory -- if only the NEW coins are being sold, then you're going to see a large spike in prices. As people are going to have to pay higher and higher amounts for these coins as the demand is going to be high for the small amount of coins that are being sold.
I'm also assuming a given that demand is still high for buying as it is right now.
So, the price would skyrocket. But this isn't a realistic way to look at the market.