Can man be considered "Sinful Toward God" if he doesn't know God?

It's a simple question. Genesis 13:13 describes the reason for the destruction of Sodom and Gomorrah as such:

יג  וְאַנְשֵׁי סְדֹם, רָעִים וְחַטָּאִים, לַיהוָה, מְאֹד.

13 Now the people of Sodom were wicked and sinners against the LORD exceedingly.

But how can the people of Sodom sin against God, if they don't know God? Targum Onkelos provides an obvious answer:

וְאַנְשֵׁי סְדוֹם, בִּישִׁין בְּמָמוֹנְהוֹן וְחַיָּבִין בְּגִוְיָתְהוֹן, קֳדָם יְיָ, לַחְדָּא. 

And the people of Sodom, acted wrongly with their money, and were guilty with their bodies, before God, exceedingly.

That is, they sinned before God, not necessarily against God. Their acts were wicked, and God was not happy about this.

Targum Pseudo-Jonathan has a different approach. Going further than Onkelos in what their sins were, "against God" might either be interpreted as a description of how bad their sins were, or perhaps a description of yet another sin:

ואינשין דסדום בישין בממונהון דין לדין וחייבין בגופיהון בגילוי ערייתא ושדייות אדם זכי ופלחן פולחנא נכראה ומרדין לשמא דייי לחדא

And the people of Sodom, acted wrongly with their money in civil matters, and were guilty with their bodies regarding illicit sexual relations, and they shed innocent blood, and they prayed to foreign worship, and they rebelled against the name of God exceedingly.

I think, if they are to be blamed for "pulchana nichra'a", otherwise known as "avoda zara", it must mean they indeed did know God.

Targum Neofiti seems to combine the two:

ועמה דסדם בישין גבר לחבריה וחייבין בגילוי עריתה ובשפיכות אדמייה ובפלחנא נכרייה קדם ייי לחדה׃

The Peshitta is the closest to Onkelos, that is "before God", relevant word underlined:

ܘܐܢܫܐ ܕܣܕܘܡ ܒܝܫ̈ܝܢ ܘܚ̈ܛܝܝܢ ܛܒ ܩܕܡ ܡܪܝܐ/ܐܠܗܐ

 Rashi follows in the same way as Targum Pseudo-Jonathan, that they knew God and were rebelling against Him. They were probably getting it from the same midrash, Sifra, Bechukkothai 2. Rashi writes at the end of his comments to 13:13:

לה' מאוד - יודעים ריבונם ומתכוונים למרוד בו:

"Against God exceedingly" - They knew their master, and they intended to rebel against Him. 

 But we should keep in mind that "elohim" can also mean "powerful", as a description. I noted a few months ago that this was the approach of Shadal to Genesis 1:2 description of a divine spirit or wind. He comments:

ורוח אלהים מרחפת וגו': כתרגומו ורוחא מן קדם ה' מנשבא, ורוח אלהים ענינו רוח גדולה וחזקה. כמו כי רוח ה' נשבה בו (ישעיה מ' ז'), ישב רוחו יזלו מים (תהלים קמ"ז י"ח), נשפת ברוחך (שמות ט"ו י') וכמו הררי אל (תהלים ל"ו ז') ושלהבתיה (שיר השירים ח' ו').

"And the wind of God was blowing..." It is as its Aramaic translation, "A wind from before God was blowing..." 

"A wind of God" refers to a great and powerful wind. As in: "Because the spirit of God blows upon it." (Isaiah 40:7); "He causes His wind to blow, and the waters flow." (Psalms 147:18); "You blew with Your spirit...: (Exodus 15:10)

Similar to "mountains of God" (Psalms 36:7), or "flame of God." (Song of Songs 8:6)

I also noted how the Talmud Chagigah may have interpreted that verse the same way. Normally the verse would be read as God's spirit, some kind of mystical element, but the Talmud understands it as truly referring to wind. Chagigah 12a: "Wind and water [were created on the first day], as it says, "וְר֣וּחַ אֱלֹהִ֔ים מְרַחֶ֖פֶת עַל־פְּנֵ֥י הַמָּֽיִם". So what does it mean to be a "wind of God"? Must be a powerful  wind.

So too Shadal here. In dealing with the issue of how Sodom can be condemned for sinning against God if they don't know God, he agrees with how he sees the Baal HaTroup:

לה' מאד: נראה דעת בעל הטעמים כי לה' ענינו מאד (כמו עיר גדולה לאלהים יונה ג' ג') כי אנשי סדום לא ידעו את ה', ואיך יהיו חוטאים לה', ומכל מקום נ"ל כי ייתכן לומר שהיו חוטאים לה' גם אם לא ידעו שמו, כי היו עושים מעשים הרעים בעיניו...

 "Against God, exceedingly." It seems the accentuator understands "la-hashem" as referring to "exceedingly" (like "a great city to God" Jonah 3:3), for the people of Sodom didn't know God, so how could they sin against God? Still, I believe it possible that it could say that they were sinners against God even if they didn't know His name, as in they acted evilly in His eyes...