Please association with me 是"请你和我交往"的意思吗

yes!

association with sb
与...交往

Please association with me
请你和我交往

不是。这是一句典型中式英语，语法不通的。
你要说"请你和我交往"可以这么讲：
Please make friend with me. 让我们做朋友吧
Let's be friends.
如果问的是愿不愿做男、女朋友，可以讲
Do you want to be my boyfriend/girlfriend?
或者
I really like you. Can you be my boyfriend/girlfriend?
说法多了

shi