No, it looks like you can do what you want.

You may wish to consider doing this:

1. Go to Sams Club and get their 24 pack of PoolBrand dichlor shock.
2. Use those packs to chlorinate for the next 2 - 3 weeks. Doing so will ALSO add about 50 ppm of stabilizer to your pool
3. Use borax to keep your pH 7.4 - 7.8 (Dichlor has no initial effect on pH, but a strong acidic effect, as it's used up)
4. Raise the pH to near 7.8, when the dichlor is gone.
5. Make sure your filter is full of sand and working properly (you can do the 'DE test' to check). Note the 'clean pressure' on your filter.
6. Begin using the cal hypo in your skimmer.
7. Backwash when the pressure is up 6 - 8 psi

Adding cal hypo this way will 'auto-balance' your pH / TA / CH. The cal hypo 'debris' will end up on your filter. If your 'balance' (Saturation Index) is low, some of the calcium carbonate will dissolve, raising pH, TA, & CH. But, if your balance is high, excess calcium in the water will deposit on the existing calcium particles in your filter.

Also, the fine calcium powder tends to adsorb oils and debris from the water, and then remove it from the pool, when you backwash. Using this method on overloaded commercial pools, I've been able to achieve some remarkable increases in clarity and water quality.

Of course, you WILL need a K-2006 kit or equivalent, so you can keep an eye on the process.