Will an Icoca IC card be acceptable?

I'm coming to Japan in September for the World Cup and I am staying in Osaka. Just wondering if an Icoca card would be acceptable for travelling around even on the smaller local trains from Tamagawa and Noda etc to enable me to get to Kobe and Hanazono? I would also like to travel up to Kyoto and Wakayama hopefully being able to use this card.

No problem, ICOCA also can be used in PiTaPa(non JR-WEST), railways and buses.
https://en.wikipedia.org/wiki/PiTaPa

KTP also may better.
https://www.surutto.com/tickets/kansai_thru_english.html

If I am there for two weeks am I able to buy multiple Kansai Thru Passes?

The ICOCA card services JR trains in the regions of Hiroshima, Kyoto, Osaka, and Okayama. This card covers a slightly larger area than the other prepaid IC cards and is also compatible with some minor local cards, such as the Paspy Card in Hiroshima: https://www.jrailpass.com/blog/using-japanese-ic-cards#ICOCA_card

Thanks Kyle, so the ICOCA card can be used on smaller/local trains and buses as well as JR trains, am I right?

Exactly, Cameron. The ICOCA can be used on JR, subway, bus transportation and also for shopping in the Kansai Area.

Excellent, that sounds the most appropriate for me. I take it you have to pay extra for the use of bullet trains?

Yes, to use bullet trains you should buy a separate basic fare ticket // limited express ticket, as ICOCA cannot be used for it.

Excellent, thanks for your help :)