You shouldn’t need to put it in test mode. You can copy the test and live API keys both from your Stripe account and then paste it in the plugin’s settings. Do you have the test API keys set/saved in the settings?:
General Settings Configuration of the Accept Stripe Payments Plugin
Even if you need to setup a webhook in testmode, you can do that very quickly by going to test mode and creating the hook and then switching back to live (should take only 5 seconds). You can do that at a time of the day when the site goes through a quiet period.
The only guideline is to use latest version of any browser. Then it will work fine. If a browser version is older than 2 years (for example) then there is no guarantee since we don’t test for such old versions. Latest browser version should be used for security reasons also.