All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is an act of Sunnah that the person suffering from urinary incontinence doesn`t go early to Friday prayer; rather, it is recommended that he reaches the Masjid at the time of Khutbah (Sermon) because he has a valid excuse for doing so. "It is recommended for the Imam not to go early to the Masjid on Friday; rather, he should delay his arrival till it`s time to deliver the Khutbah, following in the teps of the Prophet (PBUH) and his rightly guided Caliphs. This was also mentioned by An-Nawawi in his book "Al-Majmou`." The same rule applies to the one suffering from urinary incontinence." {Nehayat Al-Mohtajj, 7/152}.
However, if such person did go early to the Friday prayer, then there is no harm in that provided that he does Wudoo` after the time for the prayer begins. This is because Muslim scholars have excused him from praying right after Wudoo`. Therefore, he doesn`t have to do Wudoo` again and his first Wudoo` is still valid. "
The woman who is suffering from Istihaadah [Non-menstrual vaginal bleeding] should pray right after Wudoo`. However, if she did Wudoo` after the time of prayer had begun, but offered the prayer at the end of that time-due to an excuse such as waiting for Athan to end, finding Qiblah, covering Awrah (Private parts), going to the Masjid for Friday prayer and the like, then there is no harm in that." {Al-Ikna` Fi Hal Alfad Abi Shoja`, 1/47}.
In conclusion, there is no harm if you (Asker) do Wudoo` after the time for Friday prayer begins, listen to the Khutbah, then pray with the congregation. And Allah knows best.