Yes, Your email still can be accessed
The hacker can first hack into your computer, without your AV (antivirus) detecting it. No worries, most likely its will be detected and deleted or quarantined by your AV. If you update it daily, use AV like Kaspersky, Bitdefender, AVG. I recommend Kaspersky. It will install a keylogger which will record anything use type.
The keylogger will note down easpecially the accounts you log into like Email, Bank Accounts, Payments, Credit Card number that you used for online shopping.... etc.
Also it take information about your computer like name, users,etc. most important your ip address and mac address which identifies your computer. The malware can also take screenshots and then crash your computer.