Can I include conditional logic in VS Code snippets?

The short answer is that you cannot do that kind of thing in a standard vscode snippet because it cannot dynamically evaluate any input outside of its designated variables with some limited workarounds like I'll mention next.

You might - I and others have written answers on SO about his - type your various case values first and then trigger a snippet tat would transform them into a switch statement. It is sort of doing it backwords but it might be possible.

There are extensions, however, that do allow you to evaluate javascript right in a snippet or setting and output the result. macro-commander is one such extension. I'll show another simpler extension doing what you want: HyperSnips.

In your javascript.hsnips:

snippet `switch(\d)` "add number of cases to a switch statement" A
``
let numCases = Number(m[1])     // 'm' is an array of regex capture groups
let caseString = ''

if (numCases) {       // if not 'switch0'
    let tabStopNum = 1
    caseString = `switch (\${${tabStopNum++}:key}) {\n`

    for (let index = 0; index < m[1]; index++) {
        caseString += `\tcase \${${tabStopNum++}:value}:\n\t\t\$${tabStopNum++}\n`
        caseString += '\t\tbreak;\n\n'
    }

    caseString += '\tdefault:\n'
    caseString += '\t\tbreak;\n}\n'
}
rv = `${caseString}`       // return value
``
endsnippet

The trickiest part was getting the unknown number of tabstops to work correctly. This is how I did it:

\${${tabStopNum++}:key}

which will resolve to ${n:defaultValue} where n gets incremented every time a tabstop is inserted. And :defaultValue is an optional default value to that tabstop. If you don't need a defaultValue just use \$${tabStopNum++} there.

See https://stackoverflow.com/a/62562886/836330 for more info on how to set up HyperSnips.