Dan,
If you have an English page that is also available on Turkish (same content but rewritten/translated) then an hreflang tag is recommended, not mandatory, but recommended. Although as you said you are already writing in Turkish and geotargeting in GWT, there are other engines too, that regardless their market share, shouldn't be overlooked.
HOWEVER, if you have a page in English not matching a Turkish page, then you don't need the hreflang in that page. The tag is only used when the same content is available on other language/location to tell engines which version they should serve.
What you mention about using x-default and removing the canonical is nonsense. Those are 2 different things and one would not interfere with the other. The plugin I recommended does not mess with Yoast, leaving the canonicals as they should be and adding the hrefland tags as specifies. Check this example on my site English and Spanish using both Yoast and the hreflang Manager plugin:
Check the source code, both have their canonicals and hreflang tags just fine. We chose to use the English version as the default, as you can see in the x-default.
The hreflang tags should be used only when the content is the same (but targeted to a different audience). Of course of the translation from one language to the other some lines must be rewritten to make sense.
In my example, I used two very similar (if not the same langs), however there are things that change, but those are minimal (take as an example a car "hood", in England a "bonnet"). As those are such minimal changes, I don't think a specific version for GB is needed if you are already serving a US version (that's up to you). In that case (1 english version to all english speakers), you only specify the language, instead of the Language and Region:
<link rel="<a class="attribute-value">alternate</a>" href="http://www.example.com" hreflang="<a class="attribute-value">en</a>"/>
Now, just to make sure we have an example that DOES apply a different GEO in en-US and en-GB, could be a page that explains what are car repair centers, plus below it shows a list of repair centers. In these scenario, the content is the same, but the list of repair centers change, you would like to display those in GB to your GB audience (still, from my point of view, useless, but was just an example).
Hope that clears it up