No, they can't. If your landlord wants to kick you out of their apartment, they must go through the entire eviction process—including going to court and winning the case. And they can't start the eviction process in the first place unless they have just cause. Generally, your landlord has just cause to evict you if you repeatedly fail to abide by the terms of your lease agreement, or if you are doing something illegal on the property (like selling drugs, for example).
Even if they have just cause, your landlord is still required to follow the proper procedure when evicting you. If they don't follow the rules exactly, then you get to stay until they go through the process properly. Kicking you out of the property without just cause or without following the proper procedure is illegal, and violates your rights as a tenant.
The only situation where a landlord does have the right to make you leave without an eviction notice is if they need to make a repair to keep up with housing codes. In this case, they'd actually be constructively evicting you. You definitely wouldn't be liable for any rent payments, and they should also compensate you for relocation costs.
The information provided on this website does not, and is not intended to, constitute legal advice.