Sorry, but from the Shulchan Aruch and Simla Chadasha (below) it seems signing does not count for Brochois.
But for prayer see my answer https://judaism.stackexchange.com/a/63904/5120
You can answer Omain if you did not hear anything only you know what the Brocho is about. See source below (if too much time did not pass).
The Bais Yosef 124.8 brings the story of the synagogue in Alexandria as a proof.
... It has been taught, R. Judah stated, He who has not seen the double colonnade 20 Egypt 21 of Alexandria in has never seen the glory of Israel. It was said that it was like a huge basilica, one colonnade within the other, and it sometimes held 22 24 twice the number of people that went forth from Egypt. 23 There were in it seventy-one cathedras of gold, corresponding to the seventy-one members of the Great Sanhedrin, not one of them containing less than twenty-one 25 talents of gold, and a wooden platform in the middle upon which the attendant of the Synagogue stood with a scarf in his hand. When the time came to answer Amen, 26 he waved his scarf and all the congregation 27 duly responded. ...
20 ** i.e., the basilica-synagogue.
21 From the foundation of the city by Alexander the Great in 332 B.C.E., the Jews formed an important section of the population with their own places of worship and other rights and privileges.
22 Cur. ed. in parenthesis, ‘600,000 X 600,000’.
23 I.e., 1,200,000.
24 Bah read ‘elders’ for ‘members of... Sanhedrin’.
25 The reading ‘twenty-one myriads’ of cur. edd. is deleted by Elijah Wilna.
26 When e.g., the Reader concluded a benediction.
27 To whom owing to the huge size of the Synagogue, the reader's voice was inaudible.
But according to the Shulchan Aruch you are not obligated to, since you did not hear the Brocho (oh 215.2)
But from the Shulchan Aruch Harav 215.2 it seems you are obligated to say Omain even if you did not hear it at all (signs are not necessary) (if you know what it was about)
אבל אחר ברכת אדם אחר מישראל חובה לענות אמן אע"פ שהוא אינו מחויב בברכה זו כלל ...או אפילו לא שמעה כלל רק שהוא יודע איזו ברכה היא שלא תהא אמן יתומה כמ"ש בסי' קכ"ד(סעיף יא)...
It seems the Mishna Berrura 115.6 (below) brings that the ח''א כלל ו (סוף) א proved if they know what Brocho he should say Omain (but I do not see that he should but only that he could.)
שלא שמע כולה - אלא שמע רק שמזכיר השם וסוף הברכה חייב לענות אמן אחריו ויש שפוסקים דאפילו לא שמע רק חתימת הברכה צריך לענות אמן [א"ר] ועיין בח"א שהכריח דאפילו דעה הראשונה מודה היכא שיודע על איזה ברכה הוא עונה דצריך לענות וכדלעיל בסימן קכ"ד ס"ח בהג"ה ע"ש:
Shar Haziun 215.7 on the Mishna Berurah brings the source (ריא''ז בפרק ג') that even you did not hear at all you are allowed to say Omain.
The reason you need to hear it is to be sure you are not answering Omain to something against G-d, (see source below) (we maybe can not trust the one making the blessing) but if others hear it so we probably can trust them.
Mishna Brochois 8.8
...Respond "Amen" after a Jew blesses, and do not respond "Amen" after a Cuthite blesses until one has heard the whole blessing.
But you can not use that person's Brocho for yourself (you need your own Brocho).
From Simla Hadasha 1.32 and Shulchan Aruch yd 1.6the English they but by the end of 1.5 (probably by accident) if you do not hear the Brocho even if you made it yourself it does not count (but if you are not deaf just dumb then the Brocho that you hear might count as you said it)