Well, gee, I should hope so. Since most replacement form, which you are signing, clearly say to wait until new coverage is issued.
As to your question about RNA. You'll just need to keep checking your commission statement. The first clue you will have that it has been approved is when it shows up paid. Generally that takes about 2 or 3 business days after the PHI is completed.
What you can do is have the client call the current company and switch it to direct bill. The policy won't cancel that way. It will just go into grace period and give them a chance to pay should RNA not approve them. Some companies do require several days notice to switch from EFT, so better do it now than later.
On replacements, I fill out the replacement form and will assist the client in stopping the draft but I never cancel the policy... Let it run through the grace period and lapse. That benefited one clinet's widow immensely as her husband died during the grace period of the old policy.. Both polices paid..