Yes, it appears to be agate. It is one of the reasons they cut them open to reveal the banding. The red and yellow staining, the lack of cracks, the host rock being pitted like an old potato. Agates tend to weather but they are so hard the host rock wears away revealing the beautiful banding over time, when they cannot see the banding, they polish or cut them.
There is a banded agate stuck in this puddingstone, it is black or dark purple with red stripes. It is an example of conglomerate rock, with banded agate Hard to see, you'll have to locate it and enlarge. It is in a 250 lb. puddingstone. The red stone is jasper, the white stones are quartz.