to a certain extent yes, but only to the charge, not the sentence. for example, if the defence say "i will plead guilty to manslaughter but not murder" (at the extreme) then the prosecution will consider their evidence and whether the sentence is likely to be that different and may then amend their charge. however once the new charge is put and the defence plead guilty, the sentencing is entirely the choice of the judiciary who sentence on the facts. The prosecution have no say in sentencing, and the judiciary should not take into account the fact that the charge has changed, they sentence solely on the charge before them. However, if the prosecution believe their original charge will stand because the quality of their evidence is overwhelming (for example) then they may decide to stick with the original charge. It all depends on the prosecutor, how the police have charged (they may have charged too high in the first place), quality of evidence, liklihood of conviction and likely sentence if found guilty.....does that make sense? (i can try again if not )
FWIW the most likely charges to be amended (IME) are abh down to common assault (where for example there is no medical evidence sustaining the complainant'S version of events), dangerous driving down to careless driving, and handling stolen goods down to theft.
HTH