Will changes I make in Custom Clean be stored if I use Health Check later?

Changes made in Custom Clean don't get transferred to Health Check:

Health Check’s rules are independent of other cleaning options:

Health Check always uses CCleaner's recommended settings when cleaning unless they are customized (while using Health Check) at the time of cleaning.

If you want more in-depth cleaning options (and customization):

CCleaner's Custom Clean gives you more cleaning options and flexibility, ideal if you're an advanced user. Go to Custom Clean and click Analyze and then Clean. You can also set either Custom Clean or Health Check as your CCleaner Home Screen in  Options > Settings.