I think it's an interesting question (or really, set of questions) that you pose . . . difficult to answer in many respects, but I'll at least try to begin, based on my own limited experience (aikido many years ago, Chinese martial arts more recently with a focus on taiji training methods). I was trying to get at the same kind of comparison and contrast in this thread:
"Different training methods . . . same skills?"
looking at the examples and respective arts of Liu Chengde (Chen taijiquan) and Akuzawa Minoru (Aunkai). I think one of the problems with that thread, though, is it's attempting to compare/contrast the broad range of training practices that make up the two systems.
It's good to focus on one specific practice--like pushing--when comparing and contrasting. In looking at the aikido exemplars you list, I'm wondering if yiquan more than taijiquan might be a better comparison (from among the Chinese arts I'm familiar with). I think Yiquan would have been more fruitful to compare with Aunkai than Chen taijiquan in my earlier thread, in the sense that Yiquan has more core practices aimed directly at developing basic attributes than taijiquan's emphasis on solo form sequences.
In my experience, taijiquan skill is difficult to pursue because its training is hit-or-miss. The chansi (silk-reeling) drills are a modern development (post-WW2) intended to more systematically train a key movement and coordination attribute (silk-reeling) to weave back into the solo forms. Even highly-skilled teachers trained in the traditional way (heavy emphasis on solo form sequences) acknowledge the value of chansi drills.
Wang Xiangzhai, yiquan's developer, explored a wide range of Chinese martial arts and fighters in trying to distill essential attributes and develop focused practices (analogous to chansi exercises) to train them. The attitude expressed in his writings and training philosophy strongly reminds me of Akuzawa Minoru's outlook.
And, curious as it may sound, I think Ueshiba Morihei was also trying, in his own inimitable way, to develop training practices that worked to develop core attributes of internal strength skill that he'd felt in his own primary teacher, Takeda Sokaku. Ueshiba also continued to develop and distill what he'd felt in engaging with Takeda as well as what he'd been overtly taught. Some of those specific practices must certainly continue in today's various lines of aikido, but with the practical context missing or never learned--"hidden in plain sight," like Ellis Amdur writes--or in related practices developed by Ueshiba's leading students--like certain facets of Tohei's teaching that Mike Sigman has posted about.
So, with respect to pushing practice and its context in yiquan, it can be regarded as part of "shi li" or strength testing, and also involved in yiquan's practice of pushing hands. For static pushing (one person being pushed on) it is definitely a test of alignment, balance and frame contraction/expansion for the pushee, but--in my experience, anyways--can also reveal things for the pusher. The purpose of moving push-hands in yiquan is similar in some respects to taiji push-hands, but "yielding" is not emphasized so much as sensing then moving right into application (which can be explosive).
Yiquan isn't my main practice, though. For a better idea of the progressive yiquan curriculum, look at
Yiquan push-hands practice is described here:
Wang Binkui demonstrates a variety of yiquan's solo practices, followed by brief push-hands in the last five seconds of this clip:
There is a lot of material out there on Yiquan which provides context for specific pushing practice. I'd also like to point people to a training blog being written this summer by a fellow who flew to Beijing specifically to learn and train Yiquan working directly with one of the best teachers of the art in the world today. It's definitely worth following his insights, frustrations, and experience of Beijing today: http://cattanga.typepad.com/see_otter_yiquan/
So is pushing in yiquan indicative of the kind of internal skill(s) shown by Ueshiba or some of his leading disciples? Frankly I don't know. For me, this kind of discussion is most fruitful when focusing on a specific training practice or set of practices . . . things we can practice and feel and play with directly . . . not so much with ambiguous and largely untestable (on this forum, anyways) hypothesizing about biophysical mechanisms underlying various displays of internal strength skill.
For a persevering and open-minded aikido practitioner, the training practices and training results of yiquan may suggest modifications or improvements in his/her aikido training practices that could recharge their aikido training. I really believe that is what Dan Harden is trying to do in sharing some of his insights in individual and small-group meetings with aikidoka. Similarly, workshops with Rob John (and, this November, with Rob's teacher Akuzawa) or Mike Sigman, if people really do the work following the seminars, could really be eye-opening.