Simply put, yes.
Alkalis were the first bases known to obey the Arrhenius definition of a base. Meaning alkali are soluble in water and produce hydroxide ions.
However, not all bases are soluble in water. This means that alkali substances are actually a subclass of bases.
If a substance neutralizes an acid, it is a called a base. If that substance happens to be soluble in water, than it is called an alkali.
So, as a conclusion, all alkali substances are bases, but not all bases are alkali substances.
Alkalis can also be defined as a basic salt of an alkali metal or alkaline earth metal.