Yes, signed agreements hold up in court, but they first need to be valid (before being signed). As long the agreements meet the following 4 conditions, they are valid:
A signature added to an agreement is, to put it shortly, the confirmation that you agree with the clauses and conditions.
However, the 4 conditions listed above need to be met in order for the contract/agreement to be enforceable in a court of law.
When the 4 conditions are met + your signature is added, it holds up in court!