No your light out of the fiber will be less collimated.
Also the 445nm multi mode laser diodes have uneven divergence, that is it's not a Gaussian beam like a dpss 532nm, it's a rectangle shaped beam with the fast axis divergence being much greater than the slow axis, that's the 1st issue you must overcome if you want a better beam.
Single mode fiber has a much smaller inner dia. but multi mode fiber has a much wider inner dia. which adds to the issue, but the Raycus fiber laser uses double clad fiber with the inner fiber being doped with elements such as erbium and ytterbium making it a gain medium, this is called active fiber.
In an active fiber laser your pump sources contained by the outer core drive the inner core gain medium which produces a high quality beam.