The honest answer is that it depends on how strictly Crawford County Jail runs its background checks, and the only way to know for certain is to call them directly before you show up.
When you arrive at a facility for visitation, most jails run your identification through the NCIC database, which is the national criminal information system. That check will surface your probation status regardless of which county it is in. Crawford County having stricter rules than your home county means they are more likely to flag that status and deny entry without prior approval.
The smartest move is to call the Crawford County Jail visitation department before you ever make the trip. Be upfront about your situation. Explain that you are currently on probation in another county, that your home county allows you to visit inmates without issue, and that you would like to know their specific policy and whether you can get pre-approval to visit. Proactive disclosure almost always goes better than having it surface during the check-in process at the door.
Many facilities will approve when someone comes forward honestly and demonstrates they are not trying to hide anything. The combination of transparency and a clean record in terms of no new criminal activity since the probation started makes for the strongest case. Ask specifically whether there is a waiver or approval process and who you need to speak with to get that documented before your visit.
Also check with your own probation officer before going. Some probation conditions restrict travel to other counties or contact with incarcerated individuals, and getting that cleared on your end protects you regardless of what Crawford County decides.