Seems unlikely. Entrenched defense always has the advantage, and the Russians are throwing massive amounts of troops forward without the benefit of superior artillery they enjoyed earlier in the war. Even if you leave aside issues of morale and motivation, the position favors the defenders. It's clear that the Ukrainian strategy is to absorb everything that Russia can throw at Bakhmut, inflict as many casualties as they can, fall back if they must, and then counter later in the spring when Russia's attack is exhausted and they've got a huge front to defend with worn out troops. In the same way they traded Sieverodonetsk for Kherson and Izium, Ukraine will trade Bakhmut for Melitopol if they must.
Numbers I've been seeing indicate 2:1 casualty ratio and 7:1 death ratio. Fog of war and all that, but the glum faces on Russian media certainly don't portend any great successes for Russian forces. If there were recent videos of massive slaughters of Ukrainian troops like the ones that happened earlier this month to Russian troops in Vuhledar, you can be sure that Margarita Simonyan would be showing those videos non stop, instead of complaining about NATO forces and threatening nukes for the 700th time.