Hi Marilia,
Ideally BDLS should be run immediately after the system copy is complete.
You will be running into a high risk if still the production RFCs are working and the client's logical name is still as same as production.
There is no harm in running BDLS anytime but there are high chances that the tables with Logsys, Awsys, etc., gets locked when the conversion is running.
ways to workaround this:
1. On priority, check if all external communications in this test system is disabled (productive RFCs, PI connection, printers, mails, fax nodes, webservices, etc.,)
2. Suspend all production batch jobs in this test system
select the time window where users wont be working in the system. initiate the BDLS conversion.
for faster BDLS conversion -
1. do a test BDLS conversion run and take the output of test conversion. Select the tables (which are having more entries to convert)
2. Create a temporary index on fields (logsys, awsys, whichever is in the job log).
3. split the BDLS conversion into ranges and run the conversion.