Yes you can do that. Your script opens the source table and counts how many columns are involved. Then it opens a new target table with the columns you specified and adds as many empty rows as columns you counted. Then your script loops through all of the columns and for each one extracts the column name, the units, the LCL and the UCL which you can do using "Get Name", and "Get Property". Because there can be multiple kinds of control limits stored getting the ones you want is a little tricky but doable. For each column you extract the 4 pieces of info and then pop them into the next available row in the target table.
Another way to get just the name and control limits would be to do an IR chart (if that's what you're interested in) on all columns and then use the Save Limits>to Table to get a table containing all 3 pieces of info. You would then delete unwanted rows from the table and then transpose to get a table in the form you want. You could combine this with the other method to include the units info.