Does using ConditionalAttribute also remove arguments computation?

Yes, argument evaluation is removed when DEBUG is not defined (which is typical in Release builds).

From https://docs.microsoft.com/en-us/dotnet/csharp/language-reference/language-specification/attributes#reserved-attributes:

If the symbol is defined, the call is included; otherwise, the call (including evaluation of the parameters of the call) is omitted.

Yes, everything is removed. This can be great for avoiding expensive computations that are only relevant for (say) logging, but it means you need to be careful not to remove necessary side-effects. For example:

Trace(SomethingCritical());

is very different to:

var result = SomethingCritical();
Trace(result);

or in your specific case:

DoMagic(ComputeMagic()); // everything here done only if DEBUG symbol defined

versus

var result = ComputeMagic(); // always done
DoMagic(result); // done only if DEBUG symbol defined

From the specification §17.4.2 (emphasis mine):

If the symbol is defined, the call is included; otherwise, the call (including evaluation of the receiver and parameters of the call) is omitted.