Ruby, 25 24 bytes
->a{"#{a}"!~/\D0|^\[\]/}
This is a proc that takes one argument, the array to be tested.
->a{
"#{a}" # convert argument to string
!~ # does not match the regex...
/\D0 # a non-digit (don't match "10"!) followed by a 0
| # or...
^\[\]/ # [] at the beginning of the string (signifying the empty array)
}