Does Google have any notion of how often a result is clicked for a particular search term? If so how?
Yes, when you search on a term like "hats", Google returns links to each result with parameters in it - you need to right click and copy the link to view the parameters. For example the first link returned for "hats" currently has:
To extend the question, does crafting the use of keywords on your web page in a way that makes a searcher more likely to follow the link going to improve your page rank?
Search engine users are more likely to click on search result links if they see that it's going to lead to the information, products, or services that they're searching for. By using the keywords that users might search on in your website's title and description tags, Google may use the title for the link's text, and the description for the snippet that appears below the link, which can entice the user to click on it.
Continuing with the "hats" search term and link from above, Google displays the link's text from the website's title as:
Largest Selection of Hats and Caps Online - hats.com
Hence the user will see the search term
hats and related term (i.e., synonym)
caps, which corresponds to what the user was looking for, thereby increasing the likelihood of them clicking on the link. Similarly for description, Google displays this:
The largest selection hats and caps online in the latest styles and trends. Shop hats.com for hats, caps, bags and accessories.
This also corresponds to what the user searched on, which confirms that this could be a result they're interested in clicking on.
So by having keywords in your title and description that match what search engine users are searching for and are relevant to the content of the page, will both increase the potential for users to click on your link, and for your page to rank higher when Google evaluates it.
Is it worth the effort to craft the webpage so you get those initial clicks?
If by "initial" you mean to click on them and then leave the site (aka, bounces), Google may use bounce rate as a metric to signal that the content is not relevant to user searches. So it's important that you both entice the user to click on the search results link, and to keep them on your site by providing relevant and useful content so they won't just bounce.