Re-fluff blown-in fiberglass insulation with a cellulose blower

Since cellulose insulation is compressively packaged you cannot install it without using a blowing machine. I do not recommend trying to do this by hand. "A few bags" may not qualify you for loan of a machine, but you can certainly rent one from a big box home center or an equiment rental service.

The R-factor of fiber insulation follows an inverse "U" curve. As density increases, R-factor increases--up to a point. Dense packed cellulose insulation at 3.0 to 3.5 pcf--typical installed density in closed cavities--has an R-factor of 3.9 or 4.0, compared with 3.7 or 3.8 at settled density. Fiber glass at 2.2 to 2.5 pcf may have an R-factor in excess of 4.0, compared with 2.2 to 3.1 at design density. At some point the curves for both materials turn around and R-factor decreases with greater density. For cellulose that seems to be somewhere between 3.5 and 4.0.

Cellulose (the typical, but not the only, blown in) is much less air-permeable than fiberglass. Some tests even show it works without a vapor barrier, though I certainly put one in anyway on my project using it. It also has an R-value that increases in the cold, and no seams.

Fibreglass batts are considerably more air-permeable, have seams, and have an R-value that reduces with cold temperatures - which is not great if insulating to reduce heating costs.

So: doing what you describe is both possible and better than doing nothing, but inferior to (and probably more expensive than) blowing in more cellulose. If you have a near-religious objection to more blown in, by all means level out the blown-in and add fibreglass batts, rather than not adding anything. If, (as seems unlikely from your comments) you'd like the best insulation job for your money, consider adding more blown in.