Bottom-up approaches start analyzing a text by first determining the original intent of the human author of a text. From there, they use inductive reasoning to construct theories of broader meanings. Top-down approaches begin with a greater truth and deduce the meaning of the text from first principles. In general, can the intent of the human author be ignored by deductive interpretations?
The simple answer is to the extent that the person making the deductions care about the original author's intent.
Let's use a legal document like a contract as a start. This is less complex as it is a human document, but it still can furnish us with a basic process of understanding an author's intent. First one must start with deduction. We must always start with deduction then use induction and deduction in combination repeatedly. We deduce it is written in English because we find English letters. Then we deduce what each word means based on a strict bias of the alphabet and dictionary. Then we use our assumptions about what we consider to be acceptable grammar to determine individual sentences. We also assume that the legal document has an overall purpose and is trying to meet established legal customs of its subject and aim.
Now we start inductive reasoning. We read the sentences and try to compile main ideas that together explain the entire document and shed light to each word chosen.
After we have reached our limits of understanding we isolate portions that do not seem to fit our conclusion and switch back to deductive reasoning. Based on our preliminary understanding we make various deductions hoping to align with the difficult statements we have not yet found a place for in the puzzle. We repeat this top-down, bottom-up, top-down iteration until we think we finally understand the original intent of the author.
With the Bible, the author is God through men, so we have authors and must use every portion of scripture to help us understand the meaning of any given text. Furthermore as human reason can't understand either author's intent without illumination of the Holy Spirit, prayer and faith must govern both our inductions and deductions if we hope to arrive at any understanding.
In the end, how much we respect the original human author's intent, I think is one of several measurements that tell us how much we understand anything about the text. The same can be said about prayer, if we ignore prayer in our search for knowledge we probably don't understand either the human author or the divine author's intent. However in either case both earnest deduction and inductions are inseparably required. Both objective critical scholastic study and true dogmatic pressures derived from previous inductions upon the text are required.
Can a person totally ignore large portions of a text by overly forcing their dogma onto it? Of course, this is what every person without faith and prayer does consistently well. Several biblical scholars seem to do nothing but enforce their unbelief on scriptures not knowing that they are filled with the faith of the original author.
No method can be purely inductive. Even the historical-grammatical method begins with the a priori assumption that the author's intent matters. In addition, anyone who devotes their time to understanding a text makes an implicit assumption that the text has a timeless meaning. The meaning assigned by the reader must be tethered to the author's meaning or why bother reading the text at all?
Under a Christological hermeneutic, there are meanings beyond what the author intends to be sure. Stories about Abraham, Isaac, and Israel give us insight into the character of Jesus. Often the human author has no idea of the weight of their words. (See John 11:51.) But the deeper meaning augments and does not contradict the proximate meaning. Good allegory follows rules and respects the author.