Yes, it is possible to run ads without a Business Manager by using your ad account only. However, things become simpler as you can access everything easily on your Business Manager - insights, analytics, managing pages, segregating accounts, and reaching a wider audience get convenient.
If you do not wish to have one, you can also use your personal Facebook account or just your ad account to run ads. But this can be tedious if you wish to expand to a larger audience or have a big organization.