I thought about this a little more and wanted to add a few things.
1.) Will you be using the vCenter Server appliance? If so, then you'll likely run into some issue configuring email alerts with no ADDS/DNS if you'll be using a mail server that exists in another domain. VMware KB: Emails sent from VMware vCenter Server Appliance 5.x are rejected
2.) Will any of the components sit on separate networks (across WAN), and will any of these networks have DNS?
3.) Since you're asking about SRM I am assuming you will have a replication/recovery target offsite somewhere? With no DNS, how do the users access the systems being run in the vSphere environment (the systems you are protecting)? Literal IP's? The idea with SRM is to be able to failover to a hotsite and do so with relative transparency to the users. Without a DNS server I'm thinking that you would probably be losing a lot of the automation in failover/failback that SRM can offer. SRM can update all of your DNS records during failover in order to redirect traffic. Without DNS I would imagine the process of updating IP's is a manual one. Hopefully someone with firsthand SRM experience can shed some light on this.
4.) Page 20 of the VCOPS implementation guide only states that domain accounts are recommended for users. Nothing about being required. I'm thinking you'll probably find a few hiccup as DNS seems to be largely assumed these days. http://www.vmware.com/pdf/vcops-5-installation-guide.pdf