Agreed that's a Uniglide freehub.There doesn't appear to be enough space left for the another sprocket. Well, maybe the sprocket but not the associated spacer. The spacing between the two smallest sprockets appears narrower than between the others. I suspect that it's missing the narrow spacer behind the small sprocket.

7speed casettes build up slightly wider than 6 speed cassettes. A 6 speed Uniglide cassette is about 2mm narrower than a 7 speed Uniglide cassette. So, you may get a bit of overhang which could cause some spacing issues to the drive side stays. This is easily solved with a drive side axle spacer and re-centring the the axle. It may also mean that thread engagement is reduced, which could result in stripping the sprocket or freehub threads, though this shouldn't be an issue unless you're a strong rider.

A better solution is to mount 7 speed Hyperglide sprochets and a Uniglide outer sprocket. The wide Hyperglide spline can be narrowed to fit the Uniglide freehub body. The Hyperglide sprockets provide improved shifting. particularly under heavy load and low rpm.

The final solution is to just replace the Uniglide body with a 7 speed Hyperglide body. Still, you'll likely need a axle spacer.