I'd recommend it, if only for the idea that putting as many forms of identification on a dog/cat as possible is a great idea.
My RR is chipped and tattooed (details here:
http://www.dog-register.co.uk/) and wears 2 tags on his collar' 1 warning he is chipped and tattooed and the other with my name, address and tel number.
I don't believe rescue centres are legally obliged to check for chips, or that they even have scanners which will find them - but if they do and it gets you and your dog back togehter then it's money well spent....
Highly recommend the tattooing as well, a great visible detterent to thieves and easily spotted by police/rescue centres, etc.