The PSR-E453 can't record digital audio. It can transmit digital audio to an attached device (computer, iPad, iPhone, etc.), which can then use appropriate software to record the audio. But the PSR-E453 can't record the audio itself.
I know you know this ("I understand … that the PSR E453 cannot do this"), but I'm clarifying in case anyone misunderstands the first part of your question ("it is possible to record digital audio … with the PSR E453"). You didn't say "on the PSR-E453," and there's a difference between "with" and "on," but sometimes the subtleties of language can be confusing.
Anyway, you should be able to record the PSR-E453's digital audio signal on an iPad.
In fact, you can do this with the earlier models (PSR-E443, PSR-E433, PSR-E423, etc.) by using an audio interface to convert the keyboard's analog audio signal into digital audio. I bought the inexpensive Behringer UCA222 audio interface on another forum member's recommendation, and it works great-- but it takes RCA stereo inputs, so you'll need an audio cable with 1/4" TRS stereo plugs on one end and RCA stereo plugs on the other. The UCA222 was $30 US when I bought it, but seems to have dropped in price to $23 US (at least for Amazom Prime members), and the audio cable was $7 US:
https://www.amazon.com/gp/product/B0023BYDHKhttps://www.amazon.com/gp/product/B000068O1K