All browsers on iOS use a Safari webview. iOS does not allow the installation of competing browser engines. So, no. It may be called chrome, it may look like chrome, but it is Safari, with all the limitations that implies (and a few extra limitations as a webview, just for good measure).

Apple does this on purpose to push people to use native apps, and then they lock down access to a market of 1 billion people to their whim of the day.

Edit: another poster pulled the trigger at the same time as me, will leave my comment for good measure.

All browsers on ios use the safari engine. Only thing chrome can do is sync your bookmarks.