In order to "cash out" on this token and convert it to bitcoin, is it necessary to have previously held an ICO in order for that token to hold any value in relation to Bitcoin?
If I understand your question correctly, you want to know if a token can have value without having gone through an ICO process or if it's the ICO that gives it it's value?
An ICO serves a couple of purposes for a project;
•It promotes the project
•It is a source of revenue for the developers
•It is also a means of getting investors in and circulating the supply.
An ICO is a way of marketing a product, you explain it's use case and how much you are selling it for (per token), this is the value it is launched with.
Note that this price does not indicate how much it would be sold on an exchange.
If you own a functioning website you can create a utility token to be used on it without an ICO and give it a determined value. But if it gets listed on an exchange, investors may avoid such altcoins, as majority of the funds are held by the developers and so it can easily be manipulated.
You can phrase the question better for a more accurate response.
ICO will serve as the process to raise funds to be used for the project's development.
In this stage, the dev team will set their token's value for the time being.
But once it is already in trading, the community will determine its price, unless the team is manipulating it in the exchanges.
And that price is usually influenced by actual use case, active users, development plans or marketing done on this project.
So even if you set price during your ICO period, this will change depending on the market's response towards your project.