I am 99.9% certain it will. Consumer cameras are all using H.264 codecs in MP4 files for 4K. Based on discussions on other forums, the AX33 makes the standard 4K format and edits well in Premier Elements, versions 13, 14 and 15.
Is this the sentence? "4k supported cameras include GoProHero 4 Black, Sony XperiaZ3V, SONY FDR-AX100 4K HANDYCAM, Panasonic DMC-GH4 (MP4 and MOV), Motorola Moto X (2014), and Xiaomi Mi4"
Note that the word "include" is used, not "are limited to". And then it lists typical and popular examples. It would be the Sony way to have the AX33 use the same formats ans the AX100. Again, I can't imagine that there would be any trouble.
Since I said 99.9%, you can cover the 0.1 percent by installing a trial version. After you know it works, then buy the serial number. FWIW, I looked up the price at B&H photo today, Black Friday. It is as cheap as it ever gets! I bought my upgrade two weeks ago because I thought it was cheap. It is $10 cheaper today!