Yeap, nothing would have changed on that account. But the same reasoning could be used to block the accession of Liechtenstein to the Confederation... except Liechstenstein's population is 10 times less that of Vorarlberg... so it indeed is a possibility.
http://archive.spectator.co.uk/article/6th-september-1919/8/the-proposed-enlargement-of-switzerland
It must not be imagined that this proposed enlargement of the Confederation by the adjunction of the Vorarlberg is a mere parish-pump affair ; it can easily be proved to be nothing of the kind. A glance at the map of Europe shows that this Austrian province, which declared its independence on Novem- ber 3rd, 1918, is a mountainous district of great strategical importance, encircled as it is by Bavaria, the Lake of Constance, Switzerland, the Principality of Liechtenstein, Austria, and now also by Italy.
We refuse Vorarlberg on various grounds :
- huge influx of german speakers that would enrage our linguistic minorities
- huge influx of catholic, we had a tiny religious civil war in 1848
- undefendable canton between Bavaria, Austria and Italy
- Germans weren't happy with this idea.
- Austrians weren't happy with this idea.
We regularly have the same mariage proposals from Alsace (FR), Aosta (IT), South Tyrol (IT), Jura (FR), Vorarlberg (AT), Ain (FR), Franches-Comtés (FR) Savoie (FR), Baden-Württemberg (DE), Varese (IT) and Como (IT). Lastly, Sardina asked for it.
By the way, we wouldn't have refused to unite with Liechtenstein, the only problem would have been the fact they are a monarchy, even if we had a prussian Neuchâtel in our Confederation for a while.
This timeline can interest you
http://www.schudak.de/timelines/liechtenstein1699-1950.html