Generally speaking the answer is No. When you delete a client there is a warning box that tells you doing this will delete and remove all data and information regarding this are you sure?
What that means is that all information regading that machine and its backups will be removed from the datatbase and the ability to browse or restore any data is lost.
Your options are to roll back the DB with a DR recovery to get the client back and then leave it that way (if this was just done today you shoudl do this) or if it was from some time ago you can do the dr restore, recover the data needed and then roll back to the latest DR. You would haev to repeat this each time you needed to do a restore as well as keep that DR backup around for the duration.
Alternatively you can merge the two databases (license required) to get the deleted client back, or you can catalogue the tape media and merge it back in (requires same merge license). Both of these senarios would only be useful if the data was stored on tapes, if it was on mag disk then it has already been deleted and cannot be recovered.