I feel like the answer should be "no" since all superfluids are not strictly BEC since they can undergo a Kosterlitz–Thouless transition in 2D, for example. I believe the ideal gas isn't superfluid, but is there any experimental evidence of a BEC without superfluid properties? I've been searching with no luck.
You can have superfluids that are not BECs and BECs that are not superfluid. Let me quote a text, "Bose-Einstein Condensation in Dilute Gases", Pethick & Smith, 2nd edition (2008), chapter 10:
Historically, the connection between superfluidity and the existence of a condensate, a macroscopically occupied quantum state, dates back to Fritz London's suggestion in 1938, as we have described in Chapter 1. However, the connection between Bose-Einstein condensation and superfluidity is a subtle one. A Bose-Einstein condensed system does not necessarily exhibit superfluidity, an example being the ideal Bose gas for which the critical velocity vanishes, as demonstrated in Sec. 10.1 below. Also lower-dimensional systems may exhibit superfluid behavior in the absence of a true condensate, as we shall see in Chapter 15.
BEC exists in any Bose systems as long as temperature is lower than critical temperature. This can be explained from Bose statistics. As for superfluid, there must be interactions between two particles. That is, in ideal bose gas, it exists BEC, but not exists superfluid. As far as I know, there are still no robust proof of relations between BEC and superfluid.