You probably wouldn't see an improvement since 380 nm is so far away from absorbing wavelengths of the absorbing compound(s) in your solvent(s). For most compounds, the width of the UV absorbance is so wide that a reference wavelength is of little use.
Can you do a blank run followed by a run with your compound? Providing the baseline drift isn't too much, you may be able to subtract the baseline drift at the wavelength of interest. This may be built into you HPLC software. Sometimes the HPLC software takes the drift into account for determining the base of the peak.
Since UV is additive, consider the baseline near your peak, even if drifting, as the starting baseline for measuring peak height or area.
John Dolan suggested adding an adsorbing material to the weak (A solvent) so that the concentration goes down as the absorbance from your B solvent goes up. Before doing this, add formic acid to both solvents.
For ref to John Dolan: http://www.sepscience.com/Information/Archive/HPLC-Solutions/1506-/HPLC-108-Causes-of-Gradient-Drift
For anyone (including Sriram) who views this post with questions about the use of "Reference Wavelengths" in HPLC, please do not use the "Reference Wavelength" feature (in most systems, it can be clicked 'OFF' all the time) until you have a complete understanding of how it works with HPLC Detectors (and then I think you will decide to turn it 'OFF'). In most cases, as implemented in the software, it will destroy your original raw data and invalidate your HPLC method. *There is a lot of inaccurate and misleading information about this feature on the web and also from the chromatography software manufacturer's. Please be careful.
Here is a link to an easy to understand article which describes the feature and the types of problems it can cause as well as other techniques to use to reduce gradient induced baseline drift. "REFERENCE WAVELENGTHS (as used in HPLC UV/VIS)"