You are correct, if the HDD is setup using the correct driver. Generally this is the case if the Bios is not changed in the process. But then you still have to verify that the partition offset (not an issue w/HDDs) is correct and you have to manually enable trim (For Win 7, no Trim in previous win Ed.).
The OP indicated that the HDD is IDE (PATA). May have been a bad assumption on my part, But the vast majority of SSDs are SATA and to run near manuf specs the bios should be in AHCI mode, not IDE mode - hense incorrect driver.
Some have been successful in this, others not. I cloned a SSD to a SSD, and still ended up redoing the Win 7 installlation.
There is another advantage: if the operating system has been in use for a year or longer - it cleans up the registry. (Unless you have programs that are a REAL bear to reload and/or have lost the installation disk/programs - IE does Wife come to mind!.