If I’ve already been summoned to court for a suit from an collection agency, can I make the payment in full without having to go to court?

It would be advisable to file an answer to the complaint (the complaint is the lawsuit attached to the summons).  If you don't timely (within the deadline set forth in the summons) file an answer to the complaint with the court and serve it by mail on the opposing party (collection agency), the collection agency will get a default judgment against you.  Then, you will need to file a motion to set aside the default.  If the court grants your motion to set aside the default, the case will then be back on track and litigation will continue.

At the law library, look for answer to complaint in the index of Pleading and Practice.  This will give your the general format for an answer to a complaint.  The answer to the complaint denies the allegations in the complaint.  At the end of the answer is the verification which you sign and date under penalty of perjury attesting to the veracity of your statements in the answer.  File the answer with an attached proof of service with the court and mail a copy to the opposing party or opposing party's attorney.  The proof of service verifies the date of mailing.  You can use a court form proof of service or you can write your own.  If you write your own proof of service, it just says that you are at least 18 and the attached documents were sent via first class mail unless stated otherwise to ___________ (name and address of opposing party or opposing party's attorney) on ___________ (date).  You sign and date at the bottom.  The date you sign should be the same as the date of mailing and the same date you file your documents with the court.

The problem with just paying the entire balance now is that it won't stop the collection agency from proceeding to obtain a default judgment  as mentioned above because the payment is late and they can tack on interest, etc.

If you contact the collection agency and they agree to dismiss the lawsuit with prejudice in exchange for you sending the full payment, that will end the matter.   Be sure to get that in writing. With prejudice means the lawsuit cannot be reinstated when dismissed.  A dismissal without prejudice means the lawsuit can be reinstated.