Can a loan go to underwriting without an appraisal?
Yes. At regulated institutions, residential transactions of $400,000 or less may use a written estimate of market value instead of a full appraisal, and cash purchases do not require an appraisal. Some government streamline refinance programs also skip the appraisal. For loans that do require one, federal rules set the transaction-value thresholds that determine whether a state certified or licensed appraiser must perform it.
Yes, some loans can proceed without an appraisal. The FHA streamline refinance, for example, does not require an appraisal. Standard FHA-insured purchase mortgages, by contrast, do require an appraisal by a state-certified appraiser listed on the FHA Appraiser Roster.
Sources: Wisconsin DSPS: Appraiser, Licensed profession page; Wisconsin DSPS: Appraiser, Licensed — Licensure by Examination.