Yes, if you pay bitcoins to a non-standard pubkey script, you can spend them in a later signature script using Eligius. But there are some conditions:
The pubkey script must be spendable. For example, a pubkey script starting with
OP_RETURN can never be spent. It's up to you to craft your non-standard script to make it spendable.
Eligius will only mine valid transactions. For example, you can't have a data push of more than 520 bytes in either the pubkey or signature script.
The IsStandard() checks check more than just op codes---they also require minimum network fees (to avoid "dust" spam) and correct transaction version numbers. Eligius still includes these parts of the IsStandard() checks.
Eligius has its own minimum fee for non-standard transactions: 0.00004096 BTC per 512 bytes according to their FAQ.
If you're going to send custom transactions, I highly recommend that you test them on Testnet first. (Testnet allows non-standard transactions.)
Note also that Bitcoin Core 0.10 will likely relax the IsStandard() rules for P2SH, making it possible to use pretty much any script you want as long as you wrap it inside P2SH. (That won't help you now, but it's a good thing to consider when developing your script.)