Ok two things, one a sort of general comment and one more a direct answer to your question.
Generally speaking, Alk is not something that will sort itself out. As consumables, Calcium and Alkalinity go hand in hand. A high calcium reading means nothing without the corresponding alkalinity reading. There's a sort of see-saw effect if you don't actively manage both parameters - if alk is low, it's not uncommon to see a high calcium reading and vice-versa. If calcium is the bricks, or building blocks, for growing corals, then alkalinity is the mortar that holds the bricks together. Or alkalinity is the money in your wallet: if you're at Home Depot and they have thousands of bricks, without money to buy the bricks, all you can do is look at them sadly and wish you could buy them.
Ok, so reef tank lesson aside, the specific answer to your question is low alk is not part of your cycle. However, as things start to grow in your tank, you will notice a draw on your alk and Ca until the point they get out of balance and then things can't pull any more Ca out of your water. So you compensate by dosing, or water changes, or reactors, or whatever your favourite way of doing it, and then you see corals and stuff grow again.
But .. having said all that ... 7dKH is in fact a natural seawater kind of reading for alk. If you look at the zeovit prescriptions for example, they recommend targetting your Alk at 7dKH since they believe there is no benefit to an elevated alk beyond NSW levels. However some people like higher Alk anyhow because it contributes to increased growth rates of stoney corals (although even softeys benefit from "good" Ca/Alk numbers - they maybe just use less of it, so you add less, but it's still important to target "good" numbers).
So: 1) It won't sort itself out, you'll need to track this number and deal with it as it fluctuates 2) It's not really part of the cycle but it will start to deplete over time, and 3) 7dKH is not really a low alkalinity reading, no need to panic as yet, it's a good number to maintain Alk at for now.
Hope this helps.