Yes you can get different results. Consider a system like this:
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| a b |
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| |
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1 2
where the base of each leg is anchored, and points "a" and "b" on the horizontal run are the same distance from the elbows. If you put the cold spring at "a", the section of piping "ab2" is more flexible (to point "a") than the section of pipe "a1". Conversely if you put the cold spring at "b", the section of piping "ba1" is more flexible (to point "b") than the section of pipe "b2". This will cause different results, on the order of a percent or two, when comparing the two locations.
If the system wasn't symmetric, the differences could be much larger. Items like expansion joints and axial stops can further complicate matters.