Is there a way to scale the combined size of the fill and the stroke to certain dimensions without affecting the thickness of the stroke?
Actually there is a way to make Illustrator include the stroke in the bounding box.
Open Edit > Preferences > General (Ctrl /Cmd + K) and tick on Use Preview Bounds.
Now the size of the object can be set including the stroke.
But, it seems to behave a bit strangely. If I change the dimensions using the mouse while holding down Shift it seems to constrain proportions like expected, but if I enter a dimension, the object doesn't constrain proportions properly. This seems like a bug or perhaps I misunderstand something.
For that reason I prefer leaving Use Preview Bounds unchecked and subtract the stroke width manually like @Scott suggests.
Funny thing is that InDesign by default includes the stroke width in the bounding box and doesn't seem to have an option to change it. But in InDesign there is no problem with constraining proportions when entering values for the dimensions.
Subtract the stroke width from your desired measurement.
So 500px - 15px = enlarge to 485px with the 15px stroke, the final dimension would be 500px (assuming stroke is aligned to center).
The bigger issue may be that scaling is always relative and never absolute. You can alter an object's dimensions easily (Via the Transform Panel or Control bar), but you can only scale by percentages.
As @Joojaa points out in comments the value fields will do the math for you. So, you can merely enter
500px-15px in the
w field and AI will calculate that for you.
Well, there's an option you have to check. Go to the Edit > preferences > General or just hit the shortcut, Ctrl + K.
Then find the option which says, Scale Stroke and Effects and just check the box.
Now every time you scale an object, the stroke and the effects will also change with it. (See the below two images for reference.)
Preferences > General > Uncheck Stroke and Effects
One way is to keep the stroke aligned inside of the object and scale through transform panel.
If align to inside provides a shape that is not required then, it is difficult to create a generic scenario that could be work for anyone, I have two ideas that can be used individually or mixed and match as required.
Manually resize the object considering that the final size of the object depends on the stroke alignment.
1) Aligned Center: Stroke Size would be added.
2) Aligned Inside: Twice the Stroke Size would be reduced.
3) Aligned Outside: Twice the Stroke Size would be added.
Use Path Offet.
1) Scale the Object to the desired size - stroke size.
2) Effects > Path > Offset Path
2) Add the Path Size
3) Object > Expand Appearance.
If none of the above works, then I would need sample files to create a script.