Yeah, more or less. Generally you would need to indicate that the school is a location, but this phrase is an exception.

Swahili more or less has an idiomatic parellel to some idiomatic phrases in English:

nita(kw)enda shule = I will go to school (i.e. I'm a student there and I'm going to go there in order to attend lessons)
nita(kw)enda shuleni = I will go to the/a school (i.e. it's simply my destination ... maybe I'm delivering a package, maybe I'm a teacher or a parent, etc., no further information is given)

This -ni suffix is a bit complicated. It's generally added to common nouns (not names of people or places) to simply indicate that we're talking about the place. Whether it means "to", "at/in" or "from" generally depends on the verb it goes with. Eg.

kwenda dukani = to go to the shop kufanya kazi dukani = to work in/at the shop
kutoka dukani = to exit/leave (from) the shop

If the place is a name of a place, you simply do nothing as the place interpretation is default.

Nitakwenda Tanzania = I'm going to Tanzania.
Tanzania kuna simba. = In Tanzania, there are lions.
Toka Tanzania! = Leave Tanzania!

With people and I suppose animals, you introduce them with kwa.

Niko kwa Sonya. = I'm at Sonya's.**

Sometimes where the verb doesn't give the right meaning, you simply add kwenda or kutoka to give the right meaning.

Ninatembea msituni. = I'm walking in the forest.
Ninatembea kwenda msituni. = I'm walking to the forest.
Ninatembea kutoka msituni** = I'm walking from the forest.

This also works with people:

Niliipata kutoka kwa Rashidi. I got it from Rashidi.