My personal experience is Yes, I scored higher on the real GMAT than any of the practice tests I took. Below is the summary of my practice test scores and the real GMAT:
Manhattan prep GMAT CAT 1, April 2018: Total 640 Q42 V35
Official Guide GMAT CAT 1, April 2018: Total 640 Q45 V34
Manhattan prep GMAT CAT 2, May 2018: Total 590 Q42 V31 (was very distracted during this test as I was going through a breakup)
Manhattan prep GMAT CAT 3, June 2018: Total 630 Q44 V32
Economist GMAT practice Test, June 2018: Total 620, Q47 V32
Veritas GMAT practice Test, June 2018: Total 670, Q49 V34
Official Guide GMAT CAT 2, July 2018: Total 680, Q49 V35 (during the Verbal section my neighbor started blasting music and I got distracted and paused the exam for a minute or so...)
GMAT 1st attempt, July 2018: Total 710, Q48 V40, IR 7
All my tests were taken in the following order of sections: Quant, Verbal, IR, AWA. My IR score of 7 in the GMAT was also the highest I ever did, on average I got 4-5 each time in the practice tests. The official guide tests are probably the best representation of your overall skill and ability.
My overall opinion is that the Quant section on the practice tests are fairly competitive and representative of the real GMAT. The scoring scale on Quant may also be accurate for practice tests. But if you look at my Verbal scores, I scored much higher on the real GMAT than on my practice tests and I also remember the Verbal section being a lot easier than the practice tests. I am not sure if these factors vary from test-to-test or location etc. But this was my experience.
I also remember feeling pretty tense and discouraged during and after the Quant section due to the difficulty of the questions and just nerves I guess. But thankfully the verbal section made up for it to boost the overall score over 700, which was my goal.
So I think its definitely possible to score higher on the real GMAT than on practice tests. If you think about it, a lot of test prep companies guarantee a certain score increase from the free practice tests if you undertake their paid test prep program. This suggests to me that the companies would tend to underestimate your score which allows them to guarantee the score increase. Thats just my thought and opinion.
Look forward to hearing other GMAT stories.