Very possible... have you ever noticed there is not Colorado River Delta??? Since there isn't, where did all the erosion product mud go?
Wind is a major erosional force in parts of the Colorado River basin. Some sediments from Colorado and Wyoming were blown as far as the Atlantic Ocean.
Much of the strata exposed in the Grand Canyon are limestone and dolomite. These rocks eventually simply would have dissolved.
http://www.talkorigins.org/indexcc/CD/CD210.html
(it all melted or blew away!)

River delta. Coloured aerial photograph of the Colorado River delta, in the Gulf of California, USA. The river is the dark hemispherical shape at the bottom of the picture. Its waters branch out (dark) like the boughs of a tree through sandbars, which are seen as the peach coloured areas.
The Mississippi
The Mississippi carries yearly in its stream many billions of tons of detritus, a large part of which is deposited in the delta. As early as 1861, Humphreys and Abbot calculated the age of the Mississippi by evaluating the detritus borne by it and the sediment deposited in the delta. They arrived at the low figure of 5000 years as the age of the delta, its birth being related to about the year 2800 before the present era. However, when at the close of the Ice Age the ice cover melted in the north, multitudinous streams must have carried an enormous amount of detritus into the Mississpippi and its tributary, the Missouiri, and for this reason the above figure, if otherwise properly calculated, must be appreciably reduced. It is assumed that when the continental ice started to melt and the Great Lakes became swollen, but the St Lawrence was still blocked by ice, the water of the basin emptied to a great extent into the Gulf of Mexico through the Mississippi. ------
