In the short term, yes, slightly. In the medium and long term, usually no, and often they help.
The initial dip: When you apply for a consolidation loan, the lender does a hard credit inquiry, which drops your score by 5 to 10 points temporarily. Opening a new account also lowers the average age of your credit accounts, which can cost another few points. Expect a 10 to 20 point dip in the first month or two.
The recovery and boost: Once the consolidation loan pays off your credit cards, your credit utilization ratio drops significantly (assuming you don't close the cards). Credit utilization (how much of your available credit you're using) accounts for about 30% of your FICO score. If your cards were maxed out at 90% utilization and the consolidation loan brings them to 0% utilization, that single factor can boost your score by 30 to 80 points within a month or two.
The net effect for most people is positive. The utilization improvement more than offsets the hard inquiry and new account impacts.
The catch: This only works if you keep the credit cards open (for the utilization benefit) but don't use them. If you consolidate $20,000 in credit card debt, keep the cards, and then run them back up, your score will eventually tank because now you have the consolidation loan balance plus new card balances. Your total debt has increased, not decreased.
If you're worried about the temptation to reuse the cards, consider a debt management plan instead. DMPs close your credit card accounts, which means a short-term score dip from reduced available credit, but you eliminate the risk of re-accumulating debt.
Long-term, the most important factor is making on-time payments on the consolidation loan. Payment history is 35% of your FICO score. Twelve months of consistent, on-time payments on the new loan builds a positive payment record that helps your score steadily climb.