Would brushing up on English grammar rules help at all with learning Polish grammar rules?
Yes. It's almost necessary to know basic linguistic definitions. Maybe you remember it from school.
Basic linguistic knowledge is almost the same in all languages (eg. difference between adverb and adjective).
could it help me with working out whether something should be genitive or accusative etc?
Not very much. But in a few ways it can help you. For example the accusative case (without preposition) is usually used when you would have a direct
object in English. The dative case (without preposition) is usually used when you would have an indirect
object in English.
Genitive case (without prep.) is often used in the same situations as in English:
cat = Kot Magdy
- My brother's
car = Samochód mojego
But apart from this it will not help you very much with the cases. But with other things.