On the premise that Allah has existed since before the prophet Muhammad walked the Earth, and that one could submit to Allah at that time as well (Ibrahim submitted to Allah against his father's wishes), could one today submit to Allah but not accept Muhammad?
No, not today. In the time before Mohammad(puh) of course yes, they had to follow the previous prophet or their nation's prophet. But not now. Why? Because, the scriptures and books before Quran are all corrupted by mankind. Today even the Christian scholars accept that the Bible is corrupted. You can find clear contradictions in Torah, Bible etc. You can't trust them 100%. You can't be sure which parts of them are genuine and which parts of them are corrupted. With this knowledge, how can you submit yourself to Allah? What is submitting? How will you know whether you submitted properly or not? You have to trust Quran, which is the final revelation. Also it is the only genuine one. It was recited by Mohammad(puh), if you don't accept him as a prophet, how can you trust Quran? If you trust Quran, then you are automatically accepting that Mohammad(puh) was the final messenger.
There are 6 pillars of faith in Islam:
- Believing that Allah is the One True God
- Believing his angels
- Believing his messengers
- Believing his books
- Believing the Hereafter
- Believing the destiny
If you extract just 1 messenger out of this list, then you have no proper faith.
Righteousness is not that you turn your faces toward the east or the west, but [true] righteousness is [in] one who believes in Allah , the Last Day, the angels, the Book, and the prophets and gives wealth, in spite of love for it, to relatives, orphans, the needy, the traveler, those who ask [for help], and for freeing slaves; [and who] establishes prayer and gives zakah; [those who] fulfill their promise when they promise; and [those who] are patient in poverty and hardship and during battle. Those are the ones who have been true, and it is those who are the righteous. (Surat Al-Baqarah 2/177)
Also Abraham(puh)'s case was somehow different to ordinary people. He become a messenger too. But there will be no messengers after Mohammad(puh), also Quran will never be corrupted by mankind.
Muhammad is not the father of [any] one of your men, but [he is] the Messenger of Allah and last of the prophets. And ever is Allah , of all things, Knowing. (Surat Al-'Aĥzāb 33/40)
Indeed, it is We who sent down the Qur'an and indeed, We will be its guardian. (Surat Al-Ĥijr 15/9)
About the authenticity of Quran, you should make more research. It is a really small area here for that. You should study Quran in order to check contradictions, rationalization etc; you should study Islam History at least brief manner to understand how it is preserved; you should study the life of Mohammad(puh) both historically and in religious concept, what he did, what he bring, what he changed etc. This is a long way I know, but there is no beautiful and true thing in the world which can be reached easily. (except memorizing Quran)
However you can search this site for quick answers, or videos of great scholars in the internet. Just be careful, critical and sure to understand true.
No. Allah has said: آمَنَ الرَّسُولُ بِمَا أُنزِلَ إِلَيْهِ مِن رَّبِّهِ وَالْمُؤْمِنُونَ ۚ كُلٌّ آمَنَ بِاللَّهِ وَمَلَائِكَتِهِ وَكُتُبِهِ وَرُسُلِهِ لَا نُفَرِّقُ بَيْنَ أَحَدٍ مِّن رُّسُلِهِ ۚ وَقَالُوا سَمِعْنَا وَأَطَعْنَا ۖ غُفْرَانَكَ رَبَّنَا وَإِلَيْكَ الْمَصِيرُ
The Messenger has believed in what was revealed to him from his Lord, and [so have] the believers. All of them have believed in Allah and His angels and His books and His messengers, [saying], "We make no distinction between any of His messengers." And they say, "We hear and we obey. [We seek] Your forgiveness, our Lord, and to You is the [final] destination."
'no distinction between the messengers' means we believe in all of them.
Every scripture points to receiving guidence from God. Once guidence from God is established the scripture has served its purpose. A person who lives his life according to man made traditions is lost. Guidence is personal and individual, the receiving of knowledge for the perfection of the individual by hearing the voice of god called conscience.