That depends on the type of email account. An account set up as IMAP will do exactly what you want. So will a Microsoft Exchange account. An account set up as POP3 will not. Most major email providers default to IMAP, or, if they are Microsoft Office 365 the default is MS Exchange. Examples of IMAP accounts include iCloud, gmail, Yahoo Mail, AOL mail. Some cable TV accounts also support IMAP.
On your phone go to Settings/Mail/Accounts. Tap on an account name and it will say at the top what kind of account it is. If it says any of the account types above it is IMAP. If it isn’t one of those it will say IMAP or POP at the top.
If the account is also set up on your Mac it should just work.