Yes, very much so -- "natural" types have been known to recommend just using baking soda instead of toothpaste.
FWIW, brushing is the more important part (even without paste it probably does most of the good), but modern toothpastes are better than baking soda because they are more abrasive and because they contain fluoride. Baking soda's main utility for toothbrushing is its abrasiveness, but it's a little too soft to be optimal.
To get the most out of your toothpaste's fluoride, spit out your toothpaste and do not immediately rinse. You don't want to swallow large amounts of toothpaste, of course, but the film does more good than harm -- https://www.nhs.uk/live-well/healthy-body/how-to-keep-your-t... "Don't rinse your mouth immediately after brushing, as it'll wash away the concentrated fluoride in the remaining toothpaste."
