After doing some research I came across this information that I believe would apply to apps used to obtain electronic signatures and any other form of electronic signatures.
In 1996 the United Nations published the UNCITRAL Model Law on Electronic Commerce. The model law was highly influential in the development of electronic signature laws around the world, including in the US.
The U.S. Code defines an electronic signature for the purpose of US law as "an electronic sound, symbol, or process, attached to or logically associated with a contract or other record and executed or adopted by a person with the intent to sign the record." It may be an electronic transmission of the document which contains the signature, as in the case of facsimile transmissions, or it may be encoded message, such as telegraphy using Morse code.
In the United States, the definition of what qualifies as an electronic signature is wide and is set out in the Uniform Electronic Transactions Act ("UETA") released by the National Conference of Commissioners on Uniform State Laws (NCCUSL) in 1999. It was influenced by ABA committee white papers and the uniform law promulgated by NCCUSL. Under UETA, the term means "an electronic sound, symbol, or process, attached to or logically associated with a record and executed or adopted by a person with the intent to sign the record." This definition and many other core concepts of UETA are echoed in the U.S. ESign Act of 2000. 47 US states, the District of Columbia, and the US Virgin Islands have enacted UETA. Only New York, Washington State, and Illinois have not enacted UETA, but each of those states has adopted its own electronic signatures statute.
Canadian law (PIPEDA) attempts to clarify the situation by first defining a generic electronic signature as "a signature that consists of one or more letters, characters, numbers or other symbols in digital form incorporated in, attached to or associated with an electronic document", then defining a secure electronic signature as an electronic signature with specific properties. PIPEDA's secure electronic signature regulations refine the definition as being a digital signature applied and verified in a specific manner.
In the European Union, the EU Directive on Electronic Signatures or the EU Electronic Signatures Directive was published in the EC Official Journal, as Directive 1999/93/EC of the European Parliament and of the Council of 13 December 1999 on a Community framework for electronic signatures (OJ No L 13 p. 12 19/1/2000).
More information can be found on the Wikipedia Page on Electronic Signatures
The following two links come from a website called EchoSign, an electronic signature company. The two links provide information on the legality of electronic signatures though you will see some company branding and information. (For clarification here, I have not used EchoSign nor am I affiliated with them.)
Here is a case, Barwick v. GEICO, that electronic signature was upheld. (Does not have to do with photography but the same theory applies to electronic signatures for model releases/contracts.)
This document mentions the laws for the US, EU, UK, Canada, and Mexico.
I contacted the makers of Easy Release asking if there are any legal cases in regards to electronic model releases and this was the response I received:
I'm not aware of any direct case history. Getty Images and Alamy have
approved us for use by their contributor photographers; Getty did so after a
ten month worldwide legal review.