Not at all.
It's not always black and white, a lot of it depends on where you're starting off, what your strengths and weaknesses are. Also depends on how effective your "conversion" training is. Running a progressive structured push-up program after a few blocks of maximal strength will probably give you better results than randomly doing Bag work throughout the week with no structured progress.
That being said, the relationship between max-strength and muscular endurance is fairly well established:
https://www.ncbi.nlm.nih.gov/m/pubmed/19620916/
Hey man, a little late response. I agree with a lot of what you are saying I just want to clarify what I mean about different adaptions and why I think that the relationship between maximal strength and muscular endurance is not entirely as it's laid out. I'll use the study as an example.
Well made and solid methodology. Still it has some major flaws in how it draws its conclusion.
I think it's safe to say that it sufficiently proved that the subjects who had a higher 1RM in the benchpress, were able to do more reps with 40kg in 40 seconds. That makes total sense as it's a lower percentage of their 1RM. However, and this is where it gets interesting, that is somewhat misleading.
It's definitely true that increasing your absolute strength will increase the reps with a set weight, but, the litterature shows that maximal strength training has a negative correlation with repetitions at the same relative percentage of 1RM. This is called the strength-endurance continuum:
This is a very interesting study on that subject, by Schoenfeld and Contreras:
So while you will be able to bench the same weight more times, you will actually bench the relative percentage of your 1RM less. This also makes total sense considering the physiological changes I mentioned earlier (capillaries, oxidative enzymes, specific fiber adaptions and hypertrophy, so forth).
Does this matter? In endurance sports, yes.
Another thing that is important to note is that in the study you posted, two factors were primary in regards to benching 40kg more times. One was 1RM, another was BW. When adjusting for BW and relative strength, the correlation was actually non-significant. Meaning that absolute strength was the most important factor, ie, being heavy and strong. If you take muscular endurance out of the vacuum of benchpressing, and over to something where you have to propell yourself forward for long periods of time, increasing your BW is the worst thing you can do. There is a reason why having a BMI of about 19-20 is optimal for long distance runners:
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0090183
Point being, if you want to be an endurance athlete, don't train like a powerlifter.
Anyway, obviously it depends on the activity you want to do. We've already talked about balancing your training and using different modalities at different times! There's a lot of space between the ends of the spectrum.
If you want to geek out a bit on the strength-endurance continuum:
https://www.strengthandconditioningresearch.com/perspectives/strength-endurance-continuum/