Can people get admission in IIM A if they retake the CAT while studying at a lower ranked IIM/FMS/XLRI?

Yes, many of my friends have enrolled at IIM L after completing a year at one of the new IIMs. Your only requirement is a strong profile, a high CAT score, and a compelling reason for quitting your current business school. 

However, the opportunity cost should be considered while making this decision. This option is only practical if you come from the second generation of a new IIM or a 3 tier B-school. But you should not leave FMS or XLRI for IIM A after studying for a year in these universities. Since the opportunity cost would be too great in this circumstance.

Never consider leaving because the two years you spend there will change your perception. Newly established IIMs may, without a doubt, admit students with a lower percentile. But this is not an indication of inferior quality.