Yes, it's surprising how many things you can figure out just by being able to read hiragana and katakana. Though there are a lot of things that tend to be anomalous, like the insertion of small tsu characters in places an English speaker would not imagine a glottal stop, even assuming an English speaker who even knows what that is.
Sometimes it really takes imagination. I have a family member who has an arcade game labeled "Hangly Man" (a Pac-Man clone). It took quite a while for it to dawn on me to reverse that back to kana (HANGURI) and figure out that it was meant to be "Hungry Man."
English loan words in Japanese are so fascinating to me. Here's an example: "limited slip differential" -> リミテッド・スリップ・デフ (rimiteddo surippu defu)
(The ・ is used to separate foreign words/names when a Japanese speaker would not be able to figure it out)
This must be how Romance-language speakers feel when they see their words modified and incorporated into English.
If you want to learn the Katakana syllabary, try this website I found recently: http://katakana.training
There's also http://hiragana.training for the other syllabary.