Multiple Trackers -> do they share cookies? Or how can I track with and without cookies?

Hi,

we’d like to test the difference between regular tracking (with cookies) and tracking without cookies on a live website. I know I can use multiple trackers, as described here, but do they share the cookies, or does each tracker use its own cookies?

Meaning, would something like this even work?

var u="//matomo.example.org/";
_paq.push(['setTrackerUrl', u+'matomo.php']);
_paq.push(['setSiteId', '1']);

// the second project, where we want to track without using cookies
var websiteIdSecond = 7;
_paq.push(['addTracker', u+'matomo.php', websiteIdSecond]);
var secondTracker = Matomo.getAsyncTracker(u+'matomo.php', websiteIdSecond);
secondTracker.push(['disableCookies']);
secondTracker.push(['trackPageView']);

_paq.push(['trackPageView']);

Or what is the best way, to achieve this?