Hello. Yes, in spanish that is correct. "Tampoco" is a negation adverb and you can use it in the start and in the end. Grammatically, negation adverbs go in the end. But it works at the beginning too, specially in oral speaking. The meaning doesn't change.
For example the sentence I don't have money to eat, time either, you can write/say:
No tengo dinero para comer, tampoco tiempo.
Also, you can say: No tengo dinero para comer, tiempo tampoco.
In this case the word "no" is the first negation clause. The adverb "tampoco" works as the second clause.
I hope this will be helpful.