No! if the posting tells you to “snail” mail your application, then do so. Otherwise, it appears that you do not know who to follow directions. Remember to reply to job postings as soon as possible, usually those who apply early will get priority consideration.
Feel free to followup with an email.
Try calling their HR department to find out if they prefer it that way. However, since it’s a lot easier to email than to mail it, remember that your resume may be lost with many others applying for the same job. Since snail mail could take a while, just print out a hard copy of your resume, a letter of application if it would help, and give it to them personally. Even if it’s just the secretary or Human resources, it would show effort and willingness on your part. Good Luck