Strictly speaking there's no causality in either direction. A word's gender determines what it takes for
other words to agree with it, while the form of the word itself can be anything. A word can always be irregular.
But not every word can be irregular. Mostly the words that belong to a gender will match a set of patterns, and the words belonging to another gender will match a different set of patterns. If you're lucky, you can learn a word from some usage that makes its gender explicit (and for irregular words, this is the only way you can learn about their irregularity). But often all you have to go on is the word, and in that case, when you want to use it, you have to make a choice. You'll do that based on the form of the word.
-----
If you want some examples of how gender irregularity in nouns works, here are a few different phenomena in Latin:
- An adjective in the first/second declensions has masculine (singular) endings -us, -ī, -ō, -um, -ō, -e and feminine endings -a, -ae, -ae, -am, -ā, -a. If you see one of these endings, and you know the adjective is first/second declension¹, then you've fully specified the gender of the adjective. There are no exceptions.
- First and second declension nouns mostly follow this pattern. Lana means wool and, as the -a suffix would lead you to expect, it's feminine. Campus means field as, as the -us suffix would lead you to expect, it's masculine. What this means is that "white wool" is lana alba and "a white field" is campus albus.
- Trees are weird. They are second declension (or sometimes fourth; pretend that's not true), appearing to be masculine, but instead they're feminine. So you'd have pinus alba, a white pine tree, or quercus alba, a white oak tree.
- There's a short list of profession terms that are first declension, appearing to be feminine, but that are nevertheless masculine. So it'd be agricola albus, a white farmer, or nauta albus, a white sailor.
- What about corpus? Well, it's neuter. Corpus album, a white body. Corpus is a third declension noun, and the third declension works completely differently. The apparent -us ending is misleading; the root of this noun is actually corpor- and the suffixes, of course, belong to the third declension.
- What do you do if you run into a word you don't know how to deal with? Pretend it's normal. Manus is a Latin word that means "hand"; it appears to be masculine, but it's feminine. It turns out that referring to hands is common enough that Spanish speakers today still remember that this masculine-looking word, now mano, is actually feminine. But we may compare Biblia, which is feminine in Spanish today despite the fact that in Latin it was neuter. It's feminine now because of that -a ending.
¹ That isn't actually true; the neuter suffixes are mostly just masculine suffixes except for one that is feminine. There are no distinctive second-declension neuter suffixes. But the suffixes by themselves are sufficient to distinguish masculine gender from feminine.