As you probably have found out by now, with the OLPC "Activity" Browse, as shipped with the G1G1 laptops, the answer is NO, you can not search within Browse. I have no idea if this is already or will be fixed in later versions of Browse. I get the impression most users have installed Opera or full Firefox because of many missing features and problems with Browse.
But if one is using Browse, and just have to search the page, here is an ugly work around.
1. <ctrl>-a to select all
2. <ctrl>-c to copy
3. start activity "Write"
4. click inside the blank page where you would enter text for your document
5. <ctrl>-v to paste. You will be looking at a poor copy of the web page.
6. click on "Edit" button within "Write" Activity
7. click in the search "box", it has a magnifying glass(?) in the left part, and a paint brush (wipe) in the right side of the "box", enter your search text there. click on the left and right arrows to the right of the search box to go to previous or next. If you find what you are looking for, note where you are in the document. Then go back to your Browse activity and go to the same place in the document, and look for your search text.