This strategy has been followed by many big investors for a long time. However you can buy btc and store it in coinbase wallet and as far as I'm concerned there won't be any problem. In fact i have been using coinbase wallet for many years without any danger. Moreover, hide all your information and especially mail.
But if you get a bull market then it is better to sell even buying at this time is like a big competition for you target.
Your suggestion is really nice to my understanding, but I suggest that if you want to purchase bitcoin and store your bitcoin wallet that will be protected i will advice you to use electrum wallet in which everyone is aware that it have a privacy and whenever you want to sell your bitcoin during the time of bullish market it will be very simple and easier to transfer the specific amount of coin needed directly to any exchange wallet, while it's recommendable to use Electrum wallet is as result of security of your bitcoin in the wallet