To an extent yes, but past a certain point not really. Higher end machines primarily offer better build quality/longevity, temperature management and thermal stability giving you more consistency with less effort. Higher end machines also offer more ease/speed of use when steaming milk without the wait times/anemic steam volume/pressure of lesser machines. I could care less about that as milk is for babies, lmao. Lower end machines (to a degree) are quite capable, just require a good understanding of the process and more effort involved. As the old saying goes, there is more than one way to skin a cat.
Generally speaking an espresso machine has two main functions... to regulate brew pressure and brew temperature. An espresso capable grinder should not only grind fine enough, but needs to do so in a consistent manner and offer a fair amount of adjustability in an espresso grind range as it's not a set it-forget it type of scenario.
IMHO the order of importance is fresh coffee, skill, determination, grinder and machine. The whole 'grinder is the MOST important part' mantra is B.S. to a degree. Yes grind is extremely important for espresso, but you don't have to spend a buttload for decent grind quality like some want you to believe. Some people have more $ and time than they do common sense/skill. If you don't have fresh coffee suitable for espresso, skill and determination then the equipment is pretty much useless.
I've owned/used some very good home/commercial machines/grinders and my current (and likely my last) setup is a Rancilio Silvia/Rocky combo. There are lots of unskilled whiners that complain about the temp management of the Silvia, stepped adjustment of the Rocky, blah, blah, blah... After all the equipment I've had my hands on in the last 8-9 years I'm quite satisfied with the espresso I'm getting from this setup and coffee I roast. Best part is I spent a 'whopping' $250 on the Silvia/Rocky via Craigslist. Don't be afraid to buy used if you know what to look for and don't mind a bit of cleaning/maintenance, which almost always positively offsets the investment.