Consciousness is the act of receiving and registering phenomena; attention, the act of choosing which phenomena to focus on (Thanissaro).
No. So called choiceless awareness is in the attention category and is an invention of some modern lay teachers. Equanimity (which always has an agenda) and exertion of right effort have roles in different situations depending on which is efficacious:
“He discerns that ‘When I exert a [physical, verbal, or mental] fabrication against this cause of stress, then from the fabrication of exertion there is dispassion. When I look on with equanimity at that cause of stress, then from the development of equanimity there is dispassion.’ So he exerts a fabrication against the cause of stress where there comes dispassion from the fabrication of exertion, and develops equanimity with regard to the cause of stress where there comes dispassion from the development of equanimity. Thus the stress coming from the cause of stress for which there is dispassion through the fabrication of exertion is exhausted & the stress resulting from the cause of stress for which there is dispassion through the development of equanimity is exhausted.”
—Majjhima Nikaya 101
Awareness is the sense response to conditioned reality. As concentration develops sensory perception increases. It therefore is used to describe jhana, where it is contrasted with discernment (wisdom) release (Samyutta Nikaya 41.7, Anguttara Nikaya 9.44).