Yes, Yes it’s essential.
Yes, first, in the trivial sense, if you’re doing a positive commandment, then that excludes doing something negative (might be exceptions to this). So if you are sincerely praying, then you are not doing something sinful at the same time. In a larger framework, recall that Moses lead the Israelites out into the wilderness to be away from the temptations of the pagan idols in Egypt, and thereby to focus on praise and worship of God.
As much as I have read, I can’t point to a verse in scripture that is a proof-text for the necessity for prayer and the consequences of it. The Talmud is an ancient commentary on the Jewish scriptures, and it is likely that this subject is discussed there. But, the Talmud is so big, I wouldn’t know where to start looking for the answer. Many but not all Jews consider the Talmud to be inspired. There are many variations of Judaism and each synagogue has its own beliefs and customs. It has been difficult for Jewish sects to agree on all the issues of living as a Jew in the United States, for example.
A famous rabbi, Akiva, in the second century, helped to establish the canon of Jewish scriptures and to lay down some rules to compensate for the fact that there was no Temple after 70 AD. As I understand it, When the Torah commands a sacrifice for sin, for example, today, without a Temple and a sacrificial altar, etc. Akiva and other scholars decided that PRAYER was a substitute for an animal sacrifice, which was for the expiation of sins. So…I would say that, yes, prayer is intended to enhance holiness. An observant Jew is a “better person” by adhering to all the commands of the Torah, not just in external form, but in an inner spiritual way.
So, you have to gently explore your Jewish friend’s point of view.