Having stayed at a homeless shelter does not affect your eligibility for naturalization in any way.
Under some extremely limited circumstances an individual could be considered a "public change", making him/her inadmissible and thus ineligible for an immigrant visa and adjustment of status. But after becoming an LPR this becomes irrelevant, and even for those people who could have been classified as "public charge" if they did not have a green card, this does not affect their eligibility for naturalization.
See
http://www.uscis.gov/portal/site/us...nnel=829b0a5659083210VgnVCM100000082ca60aRCRD
"Public charge does not apply in naturalization proceedings."