Short answer is yes. It's simple physics of diffusion. When cell abundance continues to increase through growth, the bloom will spread out. This will happen with or without water movement, and with or without cell motility. You can do a simple experiment to demonsrate that: Add an aliquot of dense phytoplankton very gently to a container of water without any stirring. Observe over time how that patch of phytoplankton spreads out.

Obviously, Kam W Tang is correct and simple diffusion equations could help you predict the spread of your bloom (assuming nothing else is going on, which is unlikely).I'd like add a more biological eeffect you might want to consider, which is self shading. During the bloom,  the concentration in phytoplankton will increase the extinction coefficient and decrease the available light in the water column. This will be particularly true where the phytoplankton concentration is the highest. You could thus expect the growth rate of the phytoplankton to be higher on the edges of the bloom region, which will further enhance to tendency of the bloom to spread over space.

I find this answer particularly interesting. I expect that this situation of a "best growth on the fringe" is more realistic for waters which have low or no hydrodynamism ?

I don't really know, this is still very theoritical. Except for a very calm lake or pond, it's hard for me to think of water with very low hydrodynamism (so low that the phytoplankton won't be dispersed) and you will always have other factors coming into play. Starting with the nutrient consumption that will be maximal where there is the most intense phytoplankton growth, leading to a limitation that will also push into the direction of spreading the bloom in space.