Yes it is very important that you achieve good speed if you want your site to be successful. Google announced more than a year back that sites wanting to rate for Mobile/cell phones will need to achieve acceptable performance.
You can read The 2018 report from Google. You can now access a Google service to help you assess your page speed.
I have read many blogs some wise and some less wise that also claimed page speed is a ranking feature for SEO outside of the Mobile or cell Phone area. There is however , no direct evidence i am aware of that this speed is a ranking factor in the Google algorithm or at least not directly.
It is very clear nevertheless that overall user experience is very influential in Google rankings and if you have an unusually high ( biggger than average) rate of users abandoning before the page has finished displaying then this could be a sign of problems for you, because this will almost certainly damage your Google ranking.
For a well written piece on speeds try this.
For an excellent discussion of Optimisation techniques try this Wikipaedia article
In summary, you will never rank really well on Google with a page that is not attractive and usable to the user. This will be borne out by bounce rates and other metrics that we know are being used by Google. For this reason it makes sense to ensure that your pages display quickly and accurately and are valued by your users. That obviously includes site speed as one contributing element but most certainly not a key element in its own right.
