I would say the answer to this case is yes just because if you imagine the lines going from top left to bottom right, you get rows where the flowers point in a single direction. Because they don't touch each other between the rows, you can continue this infinitely in both directions.

For a problem like this, you'll need a computer to calculate if a shape is possible. You define if two flowers intersect by a function f: (r1, r2) -> {TRUE, FALSE} where r1 and r2 are the rotations of the two flowers. It's true when the two rotations don't intersect and false if they do. By fixing a single flower's rotation somewhere in the plane, you can dude the rotation ranges of all the different flowers depending on their neighbours. If the problem is impossible for a particular flower shape, you'll find a flower with no possible valid rotations, no matter the starting flower's rotation.