The chuck will likely fling a fine(or not so fine) film of grease onto everything,including your face. I advise cleaning it of grease. Take the back plate off. There are only a few parts in a scroll chuck. You can hardly put it back together wrong. There is the scroll,and the 3 pinions to drive it,back plate and the screws that hold it on.
I just used paint thinner (odorless mineral spirits) to clean my new lathes. That Chinese cosmoline is obnoxious stuff!
It is DEFINITELY a good idea to take things apart and look for STRAY CHIPS. I have found a few inside GEARED lathe headstocks,where you don't want them to get into gears and bruise them. Clean them out with a magnet on a long dowel rod. DO THIS.
A friend once purchased a JET 14" lathe,only to find the carriage CLEAR FULL OF CHIPS. Probably sabotaged at the factory by a disgruntled employee. He had to send it back for a better model. What a PAIN!!!
Sand has also been found inside castings. You certainly don't want that! Look for sand inside any hollow castings,like the GEARED headstock and carriage(double walled,oil filled types.)
So,it does definitely pay to check everything out on ANY ASIAN LATHE. Be sure there are no chips in grease in the lead screw,either. You don't want damaged half nuts.
ALWAYS investigate a SQUEAK. Be careful to OIL the gear train behind the headstock. Some of them may well run on PLAIN CAST IRON SHAFTS,which can SIEZE UP AND WRING OFF if you do not oil them. I had this happen many years ago on my 10" Jet lathe. Fortunately,I did not require power feed to make a new shaft for the wrung off small gear to run on. I was not aware of such under engineered spots on Asian lathes back then. Actually,old South Bends were no better. You were expected to inspect and OIL every part of your lathe before going to work in a shop in the morning. And,this was considered work time,so you weren't "wasting" your PAID work time.
If you hear ANY grinding noises,investigate the headstock bearings and every where else that might still have some SAND or CHIPS in them. Do this AT ONCE. They really burn you for spare parts! A proper lathe should run nearly silently,except for the little clinking sound of gears.