It depends on how much you trust the security of Adobe's DNS hosting compared to where your DNS hosting currently takes place.
DNS security is inherently an issue of trust as the way in which the DNS system resolves your domain name to a given destination IP, and any compromise of the authoritative name server can allow an attacker to point your domain at a spoof site or service and the user may not notice (depending on whether you are using additional security such as SSL certificates etc.) Also remember that the authoritative DNS hosting company automatically gains some statistics about the resolution sources and patterns of requests to your domain which is unlikely to be an issue but should be mentioned.
With redelegation - i.e. changing the DNS hosting to another company - if you trust the overall security of the new company as much as the current one then there should be no overall security risk.
There is one small wrinkle to this - if you currently run your own authoritative DNS for the domain(s) in question and you use it to resolve hidden information (maybe an internal mail MX record that is for internal use only) and hide these specific types of resolution by filtering these resolution requests from the public internet then this will no longer be possible. This is a very rare and unusual scenario though.