Yes and no.

Yes

The German battlecruisers Scharnhorst and Gneisnau had already broken into the Atlantic in early 1941 and had sunk 22 ships between them. After their foray they were docked and undergoing repair work in Brest. Which is on the Atlantic coast of France that Bismark would have headed to. The three ships together^1 would have made a formidable striking force and the threat to Atlantic convoys would have been real.

When Bismark made her breakout attempt in May 1941 she was one of the most effective battleships in service. She was measurably ahead of her opponent HMS Prince of Wales in gunnery and her equal in most other categories. The comparable USS North Carolina had only recently been commissioned and the IJN Yamato was six months away from commissioning. The majority of the British battleship fleet dated back to the First World War. Bismark would likely have come close to matching Scharnhorst's and Gneisnau's tally had she not been intercepted.

During their operation the Scharnhorst and Gneisnau were ordered to avoid engaging British battleships and passed up attacks on two convoys because of the presence of HMS Ramillies and HMS Malaya. If the three German ships had been operating together neither of those ships would have been a deterrent to attacking the convoy they were escorting.

Even the Scharnhorst and Gneisnau alone were considered dangerous enough for the British to allocate significant resources to attacking them at Brest. Which brings us to ...

No

Brest proved to be a unsafe port for the German ships. The RAF attempted to bomb the ships almost weekly and both Scharnhorst & Gneisnau suffered significant damage^2 during these raids. Neither ship ever staged another sortie into the Atlantic. With no prospect that they could ever be repaired sufficiently to permit them to engage in offensive operations, in early 1942 these two, and Prinz Eugen, were ordered to return to Germany by sprinting up the English Channel. This they did on February 11th 1942; which was itself a major embarrassment for the British.

Given the scale of threat that would have existed had Bismark actually reached Brest the British would have been forced to tie down a significant portion of their fleet to counter any possible movements by three ships. Attacks on the ports they were docked at would have become even more intense.

It seems unlikely then that Bismark would have been able to accomplish anything significant afterwards beyond pulling British resources away from other areas. This was the nature of battleship warfare in the Second World War though. The threat of the ship just existing is enough to change the way your opponent thinks.

Summary

Left alone Bismark may have been able to sink some cargo ships on her initial voyage but once she docked at a French port she would likely have been forced to remain there. She was definitely a real threat though, one that needed to be guarded against.

[1] Plus Bismark's sailing companion, the heavy cruiser Prinz Eugen, which did make it to Brest after splitting from Bismark.

[2] Scharnhorst was actually heavily damaged by an RAF raid while at La Pallice further south from Brest.