Yes, no flowers = no fruits possible.

I did that with my portugal laurel one year--definitely reduced the seedlings. Decided a California Bay was less work and replaced the laurel.

By huge I assume you will be on a ladder.

I have spend countless hours trying to physically eradicate cherry laurel from my hillside. If I cut them back to nubs, they rebound. I have almost resorted to Roundup but it would cause runnoff issues. The roots also sucker and layer. Unfortunately a few neighbors allow it to thrive. It is planted often for a quick privacy hedge but it wants to be a tree.

I wish people would think twice about planting non-natives that reseed so freely elsewhere. It is like english ivy, bishop's weed and st. john's wort in my book. I am embarrased to admit to buying planting the bishop's weed naively.

As far as I know, there are no runoff or leaching issues with Roundup. I have used it for years.
Mike

Generally no runoff or leaching issues with Roundup, but if you're right on a wetland or in a riparian zone then you might want to consider using the aquatic formulations but you'd need a commercial applicator's license to buy those. It's not the Roundup itself but the surfactants that run off and get into water bodies. The aquatic formulations are used for controlling things like purple loosestrife and yellow flag iris and they have different surfactants.

Cutting off the flowers will reduce the amount of seeds produced but may not reduce the seedling population. Two things to consider: A, the plant will try to re-flower unless you cut it just as seeds are setting, and maybe even then. B, most plants produce way more seeds than will be able to germinate and turn into seedlings. Reducing the number of seeds set won't necessarily reduce the number that germinate and turn into seedlings. You'd have to get nearly all the potential seed to significantly reduce the number of seedlings.

But it's worth trying, definitely. Just maybe not right now, it may be better to wait a little longer so the plants have less time to put out new flowers.

I'd be very surprised to see English laurel producing another set of spikes specifically in response to pruning during its normal flowering.

Without checking, I think one of my pruning manuals says May is the prime time for annual pruning of this plant. The new growth has certainly started here.

My Portugal laurel did not rebloom; only the flower spikes were removed, they varied from fresh to faded stages.

It was said "If I cut them back to nubs, they rebound. I have almost resorted to Roundup but it would cause runnoff issues."

As long as you're taking the time to cut them off, you can apply full strength Roundup directly to the surface of the stump as a paint on application.

Basically, it's a snip-and-paint sort of thing. Thus no drift or other problems, even if near water or a wetland.

Alternatively, I might try spreading a tarp beneath the bush just before the berries drop to collect. It's newly cleared and barked there now, so I wouldn't be killing off anything else. Must check the adjacent patch of violets for seedlings. Seems to me that's one place the darn CL's seedlings don't grow.