For example, if I was learning Spanish (written with the Latin alphabet) while being a native speaker of English (also written with the Latin alphabet), is there any scientific research that confirms that learning Spanish will be faster than learning, say, Arabic (written with the Arabic script, which is completely unrelated to the Latin alphabet)? This doesn't just go for the Latin and Arabic alphabets, but really all human alphabets: Latin, Arabic, Cyrillic, Hieroglyphs, Greek, and many others.
Clearly, learning a new language with a similar writing system to your own will be easier in many important ways. Even if the pronunciation and spelling rules are completely different, simply not having to learn a new writing system is one less skill that has to be learned in your new language.
So clearly the writing system will contribute to the time it takes to learn a language. But it's far from the only consideration.
A number of languages have different script or alphabets from what you might be used to, and this can make a huge influence on whether the language is difficult to study or not.
But that site also examines many other factors that lead to the relative difficulty of learning a language.
So to directly answer your question: Does a familiar writing system lend to faster language learning? Obviously yes. But it's not the only factor!