Not at all, no.
Healing, in general, is not so great in 5e, magic or otherwise. Non-magical healing is particularly limited, the in-combat bits, like the BM's Rally are temp hp, which won't get you back into the fight if you're dropped.
Magic items were not 'assumed' in 5e design the way they were in other editions (tho 3e & 4e had optional inherent bonuses to write out assumed magic items). That is, monsters are supposedly calibrated for a party without them, but magic from party casters certainly is assumed (and, ultimately, CR is pretty bad, anyway). Also, while the bonuses of magic items were not built into Da Math like in prior WotC editions, 5e did return to giving many monsters resistance to non-magical weapons, so doing without those can be a bit of an issue, too (if you use such monsters, which is one reason I suggested leaning into no-magic and going with animals & other people as adversaries, rather than supernatural monsters).
You can certainly do the sort of no/rare magic-item NPC-casters-are-rare traditional "low magic campaigns" I mentioned above, in 5e.
But without PC full casters, a party is going to be far less capable and durable. Resources like spell slots are just too impactful to do without.