Yes, but indirectly.
Retirement funds, whether formal pension plans or mutual funds, are organizations or subsidiaries of organizations that manage funds from clients. Depending on what country they are in and depending on the legal rules they operate under, differing types of funds have different legal structures, they invest none, some, or all of their portfolios in the capital markets.
Economists generally restrict the idea of capital to things that you can touch, the exceptions being things like human or intellectual capital. A tractor is capital if it is used in production. Finance, on the other hand, treats capital as any claim on the funding of a business. That would be stocks or bonds.
When a retirement fund invests in the stocks, bonds, notes, debentures or the money market paper of a company, it is buying capital. If that is in an initial public offering, then it is the actual funder of the firm. If it then sells that claim in the secondary market, such as the New York Stock Exchange, then someone takes over that claim.
Most claims are bought in secondary markets. Economists do not treat those purchases as the purchase of capital, but finance does. If there is no new tractor, factory or software patent, then there is no capital if you are in economics. If you have a claim on a company, that is part of the capital structure of the firm in finance.
Retirement funds buy assets in the markets and hold them to pay future retirement claims for participants.
The mass withdrawal of retirement funds will only damage the economy if it interferes with the planting of seeds, the making of asphalt, the production of servers, and the building of restaurants. If it reduces the fees for stockbrokers or reduces the funding for retirement in general, then it won't damage the capital markets.
What it may do is drop the prices quite a bit.