I suppose it all depends on what level you want to reach. If you are just traveling and want to learn a few set phrases you should be ok with no knowledge of the HanZi.
I am not very experienced in learning Mandarin, but... in my opinion, I think you are going to run into trouble very quickly if you are not learning the written characters. There are just too many homonyms in Chinese (I am talking same sound AND same tone). Reading through long sentences in Pinyin with no characters to reference could become confusing very quickly. I am guessing in the end it would be faster to reach an intermediate level of spoken Chinese if you are also learning the characters at the same time.
Obviously, just like with the spoken language, you don't need to grasp the written language in its entirety to use it. It will not take you 2,200 hours before you can write "hello." Also, the first few characters you learn seem very difficult, but they get easier the more of them you know.
EDIT: OH also, if you want to cut corners. Typing is MUCH easier than writing by hand. Typing is closer to reading than writing. You might be able to get away with typing Chinese. I know some people who can hold a basic conversation on a social media app, but couldn't write the characters.