Does combining random and current time decrease probability of collision in this case?

Lets say we have 2 programs constantly generating random 53 bit numbers. First 32 bits are just system random and last 21 bits are the last bits of current timestamp. The programs probably don't have the same current timestamp, but also the generated numbers aren't compared at the time of generation. Does adding timestamp decrease probability of collision?

00000000000000000000000000000000 000000000000000000000  
random                           timestamp