Let Gbe a topological group with a left G-invariant metric dsatisfying  We show that if Gadmits a left G-invariant coarse embedding into a Hilbert space, then Gdoes not have Property (T). As an application of our main results, we show that if Gand Hare two non-trivial countable discrete groups, which admit left G-invariant coarse embeddings into a Hilbert space and  is their free product, then  has not Property (T).

left G-invariant coarse embedding, Property (T), free product.