will it operate as it is intended? yes. however, you get what you pay for: these types of cheap electronics aren't meant for longevity, and the longer they're used the more likely they are to fail.
i like to consider these cheaper thermostats as "placeholders" until you can save up to afford a more reliable (read: expensive) thermostat, e.g. VE or Herpstat.
i have a Jumpstart thermostat (essentially the same thing as this Inkbird; a cheap thermostat) that's been running with no issues for 3+ years, but i never allowed it the chance to fail on me as i replaced them as soon as i could (i still keep it just in case, but it is not in daily use).