That's a pretty simple problem. It depends on what kind of equipment you are using and you did not specify what the Desk is. But your audio flow would look like this:

Guitar --> amplifier (aux output) --> Computer Interface or recorder --> Computer DAW
..................................... |
..................................... v
...................................... --> Effects pedal board --> (effects loop return) amplifier

Greetings,

There are a number of ways to do what you are asking. First, I'll begin with some assumptions.

I'm assuming that the "effects" you are talking about are "wet" effects like chorus, reverb or delay and not overdrive or distortion which I do not consider to be an effect.

Method One:
Since we are working with "wet" effects then we do not have to use the guitarists effects but, instead, can use some of our racked effect units.

We mic up the guitar amp and send it off to our board where we will take the direct out and feed it into our DAW. The effects can be put on an Aux Send which will allow us to hear the effects without recording them.

Method Two:
In my facility, we use a Radial Pedal which splits the guitarists signal into its original high impedance output and adds a low impedance line level output. I take the line level output and record it into the DAW. This clean signal will later run through any one of the plugins we have which simulate amps, cabinets, microphone placement and effects. This way we can do whatever we wish to the guitar signal.

The other signal goes to the guitarists amp just like before and he (seldom a she) can play with the drive set on 11.

We came up with this solution because guitarists always want to record with more drive than necessary and the guitar loses its punch. To get the punch, we have to lower the gain and they hate that even though it records better.

So, those are the two ways that you can accomplish your goal but not the only two ways.

Good luck.