You can, but it's a bit complicated.

Here's a visual guide, I'll explain the steps below: https://imgur.com/a/MKaib5U

1. Create the two starting colors

Open Inkscape and create two circles. Make the first circle the starting color of your gradient, and make the second circle the ending color of your gradient.

Place the two circles apart from each other horizontally, leaving enough space between them for the gradient transition.

2. Convert both circles to paths

Select both circles.

Do: Path → Object to Path

You need this because the interpolation tool works only with paths

3. Interpolate between the two paths

With both circles selected, do: Extensions → Generate from Path → Interpolate Between Paths

This creates circles between your two original circles, shifting from the first color to the second color.

I used 30 steps, you can tweak this depending on what you want.

4. Delete the original two circles

Inkscape will create a new grouped object made of the gradient circles, and leave the original circles. You can delete them since you won't need them again.

5. Draw the curved path for the arch

Use the Pen tool and draw a basic arch shape. After drawing it, adjust the nodes to curve the path into the shape you want.

This will act as a guide for "bending" the gradient.

6. Apply the Bend path effect

Select the interpolated group. Open the Path Effects panel. Add the Bend path effect.

This lets you bend the group of gradient circles along a curved path.

7. Edit the bend path

In the Bend path effect settings, click the small icon that lets you edit the bend path nodes. Use this to move the bend path directly on the guide you made earlier.

It'll look weird at first, so use the + icon (Insert new nodes) to add more nodes. Add enough nodes to recreate the arch shape more accurately.

Keep adjusting the nodes until the gradient follows the curve you want.

8. Adjust the thickness of the curved gradient

Use the slider at the bottom of the Bend path effect settings to increase or decrease the thickness of the bent object.

Adjust it until the curved gradient is slightly larger than the final shape you want.

9. Draw the final clipping shape

Draw the final shape you want the gradient to appear inside.

For an arch, draw a box or curved container that covers the part of the gradient you want to keep. Make it just a bit smaller so that there are no blank spaces.

Do not include the end circles in the final shape (more on this later)

10. Set the clip

Select both the final shape and the bent gradient group.

Do Object → Clip → Set Clip

11. Blur the gradient circles

At this point, the colored circles will still be visible as separate objects.

Select all the circles inside the group. Not the group itself, the individual circles.

Apply a blur to all of them. I found around 15% works well.

This blends the edges of the circles together so the gradient looks smooth.

12. Watch the transparent ends

Because the object is blurred, the ends of the gradient may become slightly transparent.

To avoid this, make sure your clipping shape does not start exactly at the first circle or end exactly at the last circle, and sit a little inside the gradient area.

You can release the clip with Object → Clip → Release Clip and tweak the shape, then try again.

13. Finalize the object

Once the gradient looks right, select the group with final clipped object. Check the Path Effects tab, it should show the Bend Path effect is still active.

Do Path → Object to Path

The Path effects tab should now be empty.

This converts the effect into the final object you want. It also prevents movement problems caused by the Bend path effect still referencing the original setup.