Should I use two single WordPress installations because of SEO?

I read somewhere that too many plugins can sometimes affect the performance of a website due to plugin conflicts, the way plugins were coded, etc. In case there is some truth in this argument, I am wondering if the following website strategy can help to solve this problem:

• Create two websites in two single WordPress installations: Storefront (site 1), WooCommerce (site 2)
• List all the products ONLY in my Storefront (site 1) and from there send users directly to the checkout page of WooCommerce (site 2)
• Hide site 2 from google search engines since this site would only be used only for checkout and back-office purposes.

I am new to the field of web development in general and WordPress in particular, so any advice on this matter would be very much appreciated!