I am not certain on this.

Usually for most formal business documents requiring a signature (such as contracts) a paper version is printed, a signature affixed, a pdf copy of the signed version is created and emailed, followed by the original signed copy by postal mail.

The more recent innovation of allowing for an "electronic signature" is sometimes accepted as well by some business and governments. However in something truly important following up with a physical copy with an ink signature while retaining a copy for your own records is the more conservative approach.

Quite clearly the Church wants to simply be certain that the application signature is yours and not a forgery.

As this is an important document I would personally follow it up with a physical signed original by postal mail just to be certain.