Writing checks as expenses or to pay an entered bill is a...
Writing checks as expenses or to pay an entered bill is acceptable practice in either type of accounting. Simply, although there is much more to it, the difference is in timing. On a basic level accrual accounting posts income when customer is billed and expenses when you are billed. Cash accounting at its basic only counts income and expenses when they enter or leave your bank account.
If you receive no bill but write a check you can do so both in cash and accrual.
There is even a third type, modified cash, which is what most businesses I know use. In that type you post an expense when you incur a charge, mostly on a card or house account, and income same as cash accounting.