Question about 3 days pay or vacate notice

[Aiko C.]

LL sent me a 3 day notice for unpaid rent. Notice is written "demanding" rent or "possession of the premises". Of course, I paid the rent. I'm curious if I move out and vacate the premises, can I then sue my landlord for illegal eviction? Or, must I wait for the legal eviction process to complete? In other words, have I been evicted if LL demands possession of the premises?

Rest of the story, if you're interested. Requested to add a tenant (new wife) and LL asked for an additional $1600 security deposit. Fine, LL within his rights. Sent me lease addendum...but I didn't sign it (this is important). More of the story, new wife didn't have SSN, only ITIN. LL rejected using ITIN and would only use SSN. Without SSN, LL said "no credit history" and asked for $1600 extra security deposit. Well, new wife has been using ITIN to establish credit including Chase and BoA bank accounts and even unsecured credit lines (credit cards) of both $2800 and $1500. Like I said, LL dismissed using ITIN - which has a credit profile. More details, ITIN credit profile can be transferred over to SSN (when obtained) by contacting the three CB's. LL put $1600 in their on-line portal and subtracted that $1600 from my June rent payment. I still paid my normal rent for June, but the total came up short of exactly the $1600. Now LL has issued pay or vacate.