Good idea but unfortunately it doesn't work like that. Report parameters are not captured as url parameters.

Take a look at some options like snapshot, Report History, Caching, default parameters.

One or a combination of these might solve your issue.

I think perhaps snapshots would be what you want but it's worth exploring them all.

In the report manager website, browsing to the "manage" setting for a report will show you where to set these options. Some are not intuitive though so best to read what they all do first.