If I got an active US Playstation plus subscription on my alternative user. Would I be able to play games online on my main user(which is a EU account) that does not have an active ps+ subscription?
PlayStation Plus benefits available to other non-subscribing users on your Primary PS4:
Online multiplayer (subject to any parental control settings on sub accounts)
Play downloaded games purchased with PlayStation Plus discount
Play downloaded IGC games
PlayStation Plus benefits not available to other users on your Primary PS4:
Purchasing PlayStation Plus discounted products from PlayStation Store
Online game save storage
Auto patch download
PlayStation Plus exclusive early access to game trial
So yes you can play PS+ games from the US account and play online, you'll miss out on several features like auto-cloud save backups, and you'll also have to log in with the US account with + to download free games (also EU/US PS+ games are occasionally different, especially on PS3). I'd strongly recommend getting PS+ on your main account rather than fussing with multiple accounts. The save data backup is nice, and the discounted games can make up for part (or all, if you buy a lot) of the subscription cost quite easily, as games are often an extra 25% or so off during sales with PS+.