That’s not gonna fit. The length would be tough to squish the connector in there at 168mm, but ultimately it’s the 69mm x 40mm dimensions that would stop it from going in the tube at all.
I may have to change my answer and say the battery you linked might fit. The image on the right is your battery at 69mm x 40mm in a 76.2mm tube. You can see the corners interfere, but the corners on batteries are always softer than a perfect square.
BR recommends these two:
The first fits easy, but the second is very close to the battery you linked and is shown in the left, which makes me think if that one fits, that there’s a good chance yours fits too. The lengths are also the same, which makes me think they were able to squish the connector in there.
We’ve found that the dimensions on Hobbykings website are not the most accurate, and the real batteries are usually slightly smaller or larger. All batteries we recommend are ones that we have purchased and test fit ourselves, and can confirm fit fine with no interference or squishing. You should NEVER squeeze the body of a soft case lipo into a housing!
The 10Ah Turnigy lipo @corndog has linked above will absolutely fit, and is currently the highest capacity off the shelf 4s lipo we have found that fits.
We have not tested the graphene lipo @sigane17 has linked, it is borderline and may or may not fit depending on how accurate Hobbykings specs are in this case.