Your learning style doesnt matter much, whether you are visual, aural, or symbolic learner, mnemonics will work for you.
On the contrary... I tend to forget mnemonics quite quickly. So no, it doesn't work for me. Repetition and understanding the radicals helps me remember a character.
Also, accent isn't to blame entirely on what you read. It depends how well you focus on your own voice and sounding native like. My professors have told me many times that my accent sounds very native, and some acquaintances of mine when I address them in Japanese when I approach them from behind have told me they expected to see a Japanese person standing there. Point being - roomaji doesn't equal an accent, self-discipline will save you from an accent (and good ears couldn't hurt, haha).
As far as structure is concerned, although it isn't a particularly complex (whoa.. I had 複雑 rolling around my head and I couldn't find the English for a moment there!) example, it is even simpler to see the construction of verbals using rooma-ji (note, it's not romaNji).
If you have the verbals: 行きます・行く and 食べます・食べる and 帰ります・帰る. How would you create rule to explain the constructions? Using rooma-ji, I feel that it is easier to explain the conversion from stem to dictionary form by explaining it as an u/ru construction. For example: the root of ikimasu = iki, labeled as an -u verbal you get iku. Tabemasu? Root=tabe, -ru verbal, taberu. Kaerimasu? Root = kaeri, -u verbal, kaeru. This comes in use when trying to explain the difference between 帰る and 変える. Both are kaeru, but knowing the root of the two: kaeri and kae, allows you to successful determine -u verbal and -ru verbal respectively, allowing the forms of kaerimasu and kaemasu to follow naturally.
Another way roomaji can help with construction is with particles. I do not know how many times I see particles attached to the ends of words like they are suffixes when improperly romanized after learning via kana/kanji - they are NOT suffixes. Compound particles/conjunctions are also more easily explained via roomaji, such as 'no de'. 'No' acts as a nominalizer, 'de' is really the gerund of desu, therefore you can get the literal translation of 'A no de B' "Being that A is the case, B", which is the equivalent of "A, so B".
Again, like I said earlier, kana/kanji are extremely important to start learning from the beginning (I wish that where I learned Japanese they put more focus on that in the beginning), but roomaji is VERY useful in understanding structure - if it is explained correctly. I highly recommend you take a look at JSL, although it is old at this point - and I do say not perfect because it DOES use roomaji through all three books (a point that my ex-classmates and I debate all the time) - Jorden had (and still has) a unique look on the Japanese language that has given me deeper insight into the structure of the language than my peers. Rather than teaching "verbs, adjectives, adverbs, etc.", she teaches "verbals, adjectivals, nominals", which are all defined by their use within the structure of a sentence. Therefore, 食べたい is not a verb "want to eat", it is an adjectival because it follows the structure of other adjectivals, like 高い: 食べたくて,食べたくない,食べたかった etc. In any case, if you're interested, the used books cost about $10 or so, here's the link to Part 1 on Amazon:
Amazon product ASIN 0300038348
One final note on the roomaji in Jorden's series, she uses the Japanese system of roomaji for the consonants: ta, ti, tu, te, to (and explains in linguistic terms how your tongue should be placed for each one and how ti is NOT the same as the English ch, nor syo the same as sho). However, her vowels are bothersome, as おう and おお are rendered the same: oo. Therefore, unless told explicitly or you know otherwise, you may have one heck of a time figuring out how to spell Tokyo and Osaka in Japanese when their romanized by Jorden as: Tookyoo and Oosaka. This, imho, is her romanization-style downside.