can I move to Office 365 keeping same email address and emails without Outlook?

Hi

Can someone please advise if this scenario is possible;

I have email hosted at ISP, address is steve@company.com. I want to migrate to Office 365 retaining this email address and also retaining all existing emails, but I don't have Outlook or other email client. Is this possible?

The plan I thought of is.....

1) Register account with Office 365 and verify domain.

2) Login to Office 365, connect existing email account and retrieve all existing emails.

3) Change MX records so that new emails are sent to Office 365.

Will this work?

Many thanks in advance!