Full Strict SSL mode and HSTS are not really related directly.
Full (Strict) SSL controls the connection from Cloudflare to your origin server. Full requires that your server have HTTPS although the certificate may not be signed, may match another domain or similar. Full (Strict) goes a step further and tells Cloudflare to validate that the certificate is trusted by a public signing authority (or you use the Origin Certificate which Cloudflare will generate free).
This one you can test safely as you can change the setting in Cloudflare for an (almost) immediate result.
HSTS is more similar to Always use HTTPS which will Redirect all requests with scheme “http” to “https”. HSTS is an instruction to the browser that says “And remember this, change all HTTP requests to HTTPS for the next ‘x’”, where x is the length of time you set. This applies to the browser, so with Cloudflare in the picture this only influences the connection from the browser to Cloudflare.
However, if you were to turn off Cloudflare then this controls how browsers talk to your server, browsers will completely refuse to use a http:// connection and will replace it with the https:// version. This can be a problem if you don’t have a proper certificate on your origin as users will get a https certificate warning (which they cannot ignore/skip) or connection warning.
I wouldn’t turn on HSTS unless you really know what you are doing and are confident that you will continue using Cloudflare OR are confident that you know how to configure your origin server to use https if needed.