In a word, no, says Adam Kuban, who tweets at @seriouseats. "Think you're adding that personal touch by setting up third-party services to automatically send direct messages to new followers?" he writes at Open Forum. "That practice usually has the opposite effect."
Most often the typical auto-DM message goes something like this, Kuban says. 'Thanks for the follow! Looking forward to connecting with you!' If you don't already know the follower, it seems disingenuous and makes them wonder if you'll be using the DM for future spam. If you do know the follower, it sends them the signal that they're getting the same impersonal response that you give to everyone else."
Instead Kuban suggest finding the key influencers in your particular space (his being the food industry). Then, whatever you do don’t bombard them with a barrage of @mentions, @replies, and DMs. Instead, follow them and RT when they write something you like.
For the time crunched, he suggests using a third-party service to schedule tweets, such as HootSuite, SocialOomph and CoTweet. But don’t be so time-crunched that you don’t spend any effort on messaging. There is no value to signing up to Twitter if you are going to blast the same message day after day, Kuban concludes.