As far as I know, pre-tensioning of anchor rods is not required by typical codes and standards (IBC, AISC, etc.)
It is a common practice in the oil and gas industry when anchoring tall towers (such as flare stacks). Guidelines given by PIP are for towers more than 150ft tall, towers with height-to-width ratios of more than 10, and for dynamic machinery such as compressors.
For pre-tensioning to be effective, you do need enough stretch length, this can be achieve through the use of anchor sleeves (wilson sleeves), or even wrapping the anchor in tape. If the anchor is not de-bonded from the concrete by use of sleeves/tape and instead a stretch length is provide by using a base plate with chairs you will run into more pre-tension loss as initially the bond between the concrete and anchor will carry some of the load but over time this bond will relieve itself until the load is truly being carried by the anchor head.
Double nuts on top of a base plate won't do anything to help with pre-tension.
Keep in mind, high strength anchors need to be used for pre-tensioning to be effective (Grade 36 will relax over time), at a minimum this should be grade 55 anchors, ideally grade 105. Also anchors tend to lose their pretension over time due to concrete creep (typical losses are in the 20% to 60% range). According to ACI 355.1R, the reduction of the initial preload can be reduced by about 30% by retensioning (1 week after initial tensioning).