PSoC Creator doesn't support WiFi module and it can only be done in WICED Studio. You can configure and use SPI in either IDE as you mentioned.
Please post the last question on dual core working using WICED in the WICED community forums, they will be able to answer your question better.
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To add to Dheeraj's response, you can wait for ModusToolbox, which combines both PSoC 6 and WICED development environment and improves on the PSoC 6 support that exist in WICED currently.
For now you can get started in WICED and then Modus is out, you can switch to it.