You can't do it the way you suggest because if you adjust the alpha component of the fill colour, you are basically adjusting the whole colour, and it will apply the same colour plus alpha to all the selected objects.
The easiest way to adjust them all together would be to use the opacity slider instead - but that will apply the opacity to the whole objects, including both fill and stroke. You don't need to group them though. You can apply opacity to a multiple selection so that it is applied to each object individually. Then grouping and ungrouping will make no difference.
Note: There is no real difference between alpha and opacity in an SVG. The alpha is applied via an opacity attribute, specifically a
fill-opacity and/or a
stroke-opacity. For the opacity slider an
opacity attribute is also applied, but it doesn't specify the fill or stroke separately and applies to the object as a whole (both fill and stroke).
If using the opacity slider method is problematic, for example if you don't want the stroke to become transparent, there is a possible work around. However, it is a bit contrived, and may not be worth the effort. I'll let you decide.
Create each shape and apply a fill colour to each with 100% alpha, set no stroke.
Duplicate all, then set the fill of the duplicates to none, and set a stroke at 100% alpha.
Basically, at this stage you will now have the same design, however the strokes and fills will be separate objects rather than single objects with a fill and stroke. Of course this increases its complexity.
Select and group each fill and stroke piece individually. Then select all and group all the objects. You can skip this step if you want, but doing this will help keep the objects in the correct order in the stack, so that fills overlay the strokes below them.
Using the Edit Paths by Nodes tool, select one of the fill objects.
Right click and choose Select same > Stroke color. This seems counter intuitive but it will select all the objects with no stroke (i.e. only the filled objects, leaving the stroked objects unselected).
You can then adjust the opacity slider to apply transparency to the filled objects only, without affecting the separate stroke objects.