No, spiritual indicates to me that you have empathy and attempt to understand both yourself and others.
Spiritual in this sense is just another way of saying "social" animal, I'm sure wolves and other social animals feel a sense of spiritualism.
It's this sense of others that lends the dim to imagine a sky daddy, but that's taking crap WAY to far.

Not necessarily any connection to religion.
I was always agnostic, yet I can feel spiritual when looking at a beautiful setting, listening to amazing music . . . anything artistic that grabs my feeling profoundly seems spiritual to me. I have never connected spirituality with religion. When people say 'Awesome' that seems to suggest a spiritual feeling. So spiritual is anything awesome, not something religious that some institution pushes at you.

To me you cannot be spiritual and atheist. Period.

I for myself always leave room for probabilities.
Mainly because it's unknown and intriguing to contemplate.